\r\n\tWe must not forget that farming requires quite different approaches and animal feeding conditions in different farming systems. It is not the same having a larger number of animals or small herds just for family needs.
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Kramer, Brian Windsor, Kenneth Carson and Larry Bellinger",authors:[{id:"71582",title:"Prof.",name:"Phillip",middleName:null,surname:"Kramer",fullName:"Phillip Kramer",slug:"phillip-kramer"},{id:"71586",title:"Prof.",name:"Larry",middleName:null,surname:"Bellinger",fullName:"Larry Bellinger",slug:"larry-bellinger"},{id:"71587",title:"Mr.",name:"Brian",middleName:null,surname:"Windsor",fullName:"Brian Windsor",slug:"brian-windsor"}]},{id:"26867",title:"Risk Factors for Aseptic Loosening Following Total Hip Arthroplasty",slug:"risk-factors-for-aseptic-loosening-following-total-hip-arthroplasty",signatures:"Scott J. MacInnes, Andrew Gordon and J. Mark Wilkinson",authors:[{id:"68458",title:"Mr.",name:"Scott",middleName:null,surname:"MacInnes",fullName:"Scott MacInnes",slug:"scott-macinnes"},{id:"69506",title:"Mr.",name:"Mark",middleName:null,surname:"Wilkinson",fullName:"Mark Wilkinson",slug:"mark-wilkinson"},{id:"74362",title:"Mr.",name:"Andrew",middleName:null,surname:"Gordon",fullName:"Andrew Gordon",slug:"andrew-gordon"}]},{id:"26868",title:"Evidence Linking Elevated Oxidative Stress and Aseptic Loosening of Hip Arthroplasty",slug:"evidence-linking-elevated-oxidative-stress-and-aseptic-loosening-of-hip-arthroplasty",signatures:"Plamen Kinov and Peter Tivchev",authors:[{id:"64690",title:"Prof.",name:"Plamen",middleName:null,surname:"Kinov",fullName:"Plamen Kinov",slug:"plamen-kinov"},{id:"66007",title:"Dr.",name:"Peter",middleName:null,surname:"Tivchev",fullName:"Peter Tivchev",slug:"peter-tivchev"}]},{id:"26869",title:"Aseptic Loosening of Total Hip Arthroplasty as a Result of Local Failure of Tissue Homeostasis",slug:"aseptic-loosening-of-total-hip-arthroplasty-as-a-result-of-local-failure-of-tissue-homeostasis",signatures:"Jiri Gallo, Yrjö T. 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Dowsey, Trisha N. Peel and Peter F.M. Choong",authors:[{id:"80820",title:"Prof.",name:"Peter",middleName:null,surname:"Choong",fullName:"Peter Choong",slug:"peter-choong"},{id:"82173",title:"Dr.",name:"Michelle",middleName:"Maree",surname:"Dowsey",fullName:"Michelle Dowsey",slug:"michelle-dowsey"},{id:"96112",title:"Dr.",name:"Trisha",middleName:null,surname:"Peel",fullName:"Trisha Peel",slug:"trisha-peel"}]},{id:"26873",title:"Infections in Hip and Knee Arthroplasty: Challenges to and Chances for the Microbiological Laboratory",slug:"infections-in-hip-and-knee-arthroplasty-challenges-to-and-chances-for-the-microbiological-laboratory",signatures:"Peter Schäfer, Bernd Fink, Dieter Sandow and Lars Frommelt",authors:[{id:"65326",title:"Dr",name:"Peter",middleName:null,surname:"Schäfer",fullName:"Peter Schäfer",slug:"peter-schafer"},{id:"73692",title:"Prof.",name:"Bernd",middleName:null,surname:"Fink",fullName:"Bernd Fink",slug:"bernd-fink"},{id:"73693",title:"Prof.",name:"Dieter",middleName:null,surname:"Sandow",fullName:"Dieter Sandow",slug:"dieter-sandow"},{id:"73694",title:"Dr",name:"Lars",middleName:"E.",surname:"Frommelt",fullName:"Lars Frommelt",slug:"lars-frommelt"}]},{id:"26874",title:"Staphylococcus Infection Associated with Arthroplasty",slug:"staphylococcus-infection-associated-with-arthroplasty",signatures:"Weisheng Ye, Wei Shang and Yaqiong Yang",authors:[{id:"64538",title:"Prof.",name:"Weisheng",middleName:null,surname:"Ye",fullName:"Weisheng Ye",slug:"weisheng-ye"},{id:"149402",title:"Dr.",name:"Wei",middleName:null,surname:"Shang",fullName:"Wei Shang",slug:"wei-shang"},{id:"149403",title:"Dr.",name:"Yaqiong",middleName:null,surname:"Yang",fullName:"Yaqiong Yang",slug:"yaqiong-yang"}]},{id:"26875",title:"Arthroplasty in HIV/SCD Carriers",slug:"arthroplasty-in-hiv-scd-carriers",signatures:"J. Bahebeck, D. Handy Eone, B. Ngo Nonga and T. Kingue Njie",authors:[{id:"66353",title:"Prof.",name:"Jean",middleName:null,surname:"Bahebeck",fullName:"Jean Bahebeck",slug:"jean-bahebeck"},{id:"149344",title:"Dr.",name:"Ndjie Kingue",middleName:null,surname:"Thompson",fullName:"Ndjie Kingue Thompson",slug:"ndjie-kingue-thompson"},{id:"149345",title:"Dr.",name:"Eone Daniel",middleName:null,surname:"Handy",fullName:"Eone Daniel Handy",slug:"eone-daniel-handy"},{id:"149346",title:"Dr.",name:"Ngo Nonga",middleName:null,surname:"Bernadette",fullName:"Ngo Nonga Bernadette",slug:"ngo-nonga-bernadette"}]},{id:"26876",title:"Cervical Disc Arthroplasty",slug:"cervical-disc-arthroplasty",signatures:"Bruce V. Darden",authors:[{id:"74274",title:"Dr.",name:"Bruce V.",middleName:null,surname:"Darden",fullName:"Bruce V. Darden",slug:"bruce-v.-darden"}]},{id:"26877",title:"Lumbar Spinal Arthroplasty: Clinical Experience",slug:"lumbar-spinal-arthroplasty-clinical-experience",signatures:"Fred H. Geisler",authors:[{id:"68455",title:"Dr.",name:"Fred",middleName:null,surname:"Geisler",fullName:"Fred Geisler",slug:"fred-geisler"}]},{id:"26878",title:"Shoulder Hemiarthroplasty in Proximal Humerus Fractures",slug:"shoulder-hemiarthroplasty-in-proximal-humerus-fractures",signatures:"José Hernández Enríquez, Xavier A. Duralde and Antonio J. Pérez Caballer",authors:[{id:"71769",title:"Dr.",name:"José",middleName:null,surname:"Hernández-Enríquez",fullName:"José Hernández-Enríquez",slug:"jose-hernandez-enriquez"},{id:"119690",title:"Dr.",name:"Xavier A",middleName:null,surname:"Duralde",fullName:"Xavier A Duralde",slug:"xavier-a-duralde"},{id:"119692",title:"Dr.",name:"Antonio J",middleName:null,surname:"Pérez Caballer",fullName:"Antonio J Pérez Caballer",slug:"antonio-j-perez-caballer"}]},{id:"26879",title:"Postoperative Therapy for Metacarpophalangeal Arthroplasty",slug:"postoperative-therapy-for-metacarpophalangeal-arthroplasty",signatures:"Nicola Massy-Westropp",authors:[{id:"64417",title:"Dr.",name:"Nicola",middleName:null,surname:"Massy-Westropp",fullName:"Nicola Massy-Westropp",slug:"nicola-massy-westropp"}]},{id:"26880",title:"Humeral Hemiarthroplasty with Spherical Glenoid Reaming: Theory and Technique of The Ream and Run Procedure",slug:"humeral-hemiarthroplasty-with-spherical-glenoid-reaming-theory-and-technique-of-the-ream-and-run-pro",signatures:"Moby Parsons",authors:[{id:"69566",title:"Dr.",name:"Moby",middleName:null,surname:"Parsons",fullName:"Moby Parsons",slug:"moby-parsons"}]},{id:"26881",title:"Development of Proprioception After Shoulder Arthroplasty",slug:"development-of-proprioception-after-shoulder-arthroplasty",signatures:"Michael W. Maier and Philip Kasten",authors:[{id:"66316",title:"Dr.",name:"Michael",middleName:"W.",surname:"Maier",fullName:"Michael Maier",slug:"michael-maier"},{id:"71292",title:"Prof.",name:"Philip",middleName:null,surname:"Kasten",fullName:"Philip Kasten",slug:"philip-kasten"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"73138",title:"Soliton and Rogue-Wave Solutions of Derivative Nonlinear Schrödinger Equation - Part 1",doi:"10.5772/intechopen.93438",slug:"soliton-and-rogue-wave-solutions-of-derivative-nonlinear-schr-dinger-equation-part-1",body:'Derivative nonlinear Schrödinger (DNLS for brevity) equation is one of the several rare kinds of integrable nonlinear models. Research of DNLS equation has not only mathematic interest and significance, but also important physical application background. It was first found that the Alfven waves in space plasma [1, 2, 3] can be modeled with DNLS equation. The modified nonlinear Schrödinger (MNLS for brevity) equation, which is used to describe the sub-picosecond pulses in single mode optical fibers [4, 5, 6], is actually a transformed version of DNLS equation. The weak nonlinear electromagnetic waves in ferromagnetic, anti-ferromagnetic, or dielectric systems [5, 6, 7, 8, 9] under external magnetic fields can also be modeled by DNLS equation.
Although DNLS equation is similar to NLS equation in form, it does not belong to the famous AKNS hierarchy at all. As is well known, a nonlinear integrable equation can be transformed to a pair of Lax equation satisfied by its Jost functions, the original nonlinear equation is only the compatibility condition of the Lax pair, that is, the so-called zero-curvature condition. Another fact had been found by some scholars that those nonlinear integrable equations which have the same first operator of the Lax pair belong to the same hierarchy and can deal with the same inverse scattering transform (IST for brevity). As a matter of fact, the DNLS equation has a squared spectral parameter of
In this chapter, we will solve the DNLS equation under two kinds of boundary condition, that is, the vanishing boundary condition (VBC for brevity) and the non-vanishing boundary condition (NVBC for brevity), by means of three different methods – the revised IST method, the Marchenko formalism, and the Hirota’s bilinear derivative method. Meanwhile, we will search for different types of special soliton solution to the DNLS equation, such as the light/dark solitons, the pure solitons, the breather-type solitons, and the rogue wave solution, in one- or multi-soliton form.
For the VBC case of DNLS equation, which is just the concerned theme of the section, some attempts and progress have been made to solve the DNLS equation. Since Kaup and Newell proposed an IST with a revision in their pioneer works [10, 11], one-soliton solution was firstly attained and several versions of raw or explicit multi-soliton solutions were also obtained by means of different approaches [12, 13, 14, 15, 16, 17, 18, 19, 20]. Huang and Chen have got a
DNLS equation for the one-dimension wave function
with VBC, where the subscripts stand for partial derivative. Eq. (1) is also called Kaup-Newell (KN for brevity) equation. Its Lax pair is given by
and
where
In the limit of
The free Jost solution is a
The Jost solutions of (4) are defined by their asymptotic behaviors as
where
Since the first Lax equation of DNLS is similar to that of NLS, there are some similar properties of the Jost solutions. The monodromy matrix
where
It is easy to find from (2) and (9) that
and
Then we can get the following reduction relation and symmetry properties
and
The asymptotic behaviors of the Jost solutions in the limit of
Then we have
In the limit
In the limit
and
Eq. (21) leads to
which expresses the conjugate of solution
On the other hand, the zeros of
where
in order to maintain that
Due to
The 2 × 1 column function
An alternative form of IST equation is proposed as
Because in the limit of
The integral path for IST of the DNLS.
where
where a factor
Taking the symmetry and reduction relation (18) and (28) into consideration, from (31) and (33), we can obtain the revised Zakharov-Shabat equation for DNLS equation with VBC, that is,
Substituting Eqs. (34) and (35) into formula (26), we thus attain the
where
Let
where
where superscript “T” represents transposition of a matrix. Then Eqs. (39) and (40) can be rewritten as
where m = 1, 2,…, N. They can be rewritten in a more compact matrix form.
Then
where
Substituting Eqs. (48), (49) into (50) and (51) and then substituting (50) and (51) into formula (36), we thus attain
where
In the subsequent chapter, we will prove that
It is obvious that formula (52) has the usual standard form of soliton solution. Here in formula (52), some algebra techniques have been used and can be found in Appendix A.1 in Part 2.
We only need to prove that Eq. (55) holds. Firstly, we define N × N matrices P1, P2, Q1, Q2, respectively, as
Then
where
where
Similarly,
where
It is easy to find a kind of permutation symmetry existed between expressions (59) and (61), that is,
Comparing (58) with (62) and making use of (63), we thus complete verification of Eq. (55). The soliton solution is surely of a typical form as that in NLS equation and can be expressed as formula (52).
The time evolution factor of the scattering data can be introduced by standard procedure [21]. Due to the fact that the second Lax operator
Then the typical soliton arguments
where
Substituting expression (64) and (65) into formula (59) and then into (58), we have
with
About the calculation of the most complicate determinant
with
The above summation obviously can be decomposed into two parts: one is extended to m1 = 0, the other is extended to
with
Here
An interesting conclusion is found that, besides a permitted well-known constant global phase factor, there is also an undetermined constant complex parameter bn0 before each of the typical soliton factor
We give two concrete examples – the one- and two-soliton solutions as illustrations of the general explicit soliton solution.
In the case of one-soliton solution, N = 1,
It is different slightly from the definition in (66) for that here
and
The complex conjugate of one-soliton solution
where
and
And we get
where
and
where
Substituting (81) and (84) into formula (52), we thus get the two-soliton solution to the DNLS equation with VBC
Once again we find that, up to a permitted global constant phase factor, the above two-soliton solution is equivalent to that gotten in Ref. [23, 24], verifying the validity of our formula of
The complex conjugate of expression (52) gives the explicit expression of N-soliton solution as
Without the loss of generality, for
As
and in the vicinity of
Here the complex constant
Introducing a typical factor
and
In the vicinity of
Here
then
Each
So as
then as
That is to say, the
Finally, we indicate that the exact
is also integrable [23] and called modified nonlinear Schrödinger (MNLS for brevity) equation. It is well known that MNLS equation well describes transmission of femtosecond pulses in optical fibers [4, 5, 6] and is related to DNLS equation by a gauge-like transformation [23] formulated as
with
with
The
The newly revised IST technique for DNLS equation with VBC supplies substantial foundation for its direct perturbation theory.
Gel’fand-Levitan-Marchenko (GLM for brevity) equations can be viewed as an integral-transformed version of IST for those integrable nonlinear equations [21, 24, 28].
In this section, a simple method is used to derive and solve Marchenko equation (or GLM equation) for DNLS E with VBC [28]. Firstly, starting from the first Lax equation, we derive two conditions to be satisfied by the kernel matrix
DNLS equation is usual expressed as
with vanishing boundary,
The first Lax equation is
In the case of
where
As usual, we introduce the integral representation,
where the superscripts d and o mean the diagonal and off-diagonal elements, respectively. According to the conventional operation in IST, the time variable is suppressed temporarily. Here
Due to the symmetry of the first Lax operator
Substitute Eq. (115) into the first Lax Eq. (111). By simply partial integration, we have the following terms:
and
Use is made of that
According to equation
Or
and the equations in the integral
Therefore, Eq. (125) gives two conditions to be satisfied by the kernel matrix
Since (122) is an identity, Eq. (123) or (124) gives the solution
In Eq. (115), the
where
We now show the kernel
Making partial derivation in (128) with respect to x and y, respectively, we obtain
By partial integrating, Eq. (131) becomes
Use is made of the fact that
We find
Since
If we choose
then
Thus, Eq. (134) becomes
Now substituting (135) into (129), we find
Making partial derivation with respect to x and y, respectively, on the l.h.s. of Eq. (138), we have
or
Now we make a weighing summation as
Hence, we have
Noticing
We find that, as long as we choose a suitable form for
Considering the dependence of the Jost solutions on the squared spectral parameter
where
As is well known, Lax equations are linear equation so that a constant factor can be introduced in its solution, that is,
When there are N simple poles
where
Here and hereafter the superscript T represents transposing of a matrix. On the other hand, we assume that
Then
Substituting (146)–(149) into the Marchenko equation (128) and (129), we have
or
here
Both of them are N × N matrices and their matrix element are, respectively, expressed as
From (151) and (152), we immediately get
from (148), (156), and (157), we have
then
and
Substituting (160) and (161) into Eq. (124), we thus attain the N-soliton solution as follows in a pure Marchenko formalism.
where
and we will prove that in (136)
By means of some linear algebraic techniques, especially the Binet-Cauchy formula for some special matrices (see the Appendices 2–3 in Part2), the determinant D and C can be expanded explicitly as a summation of all possible principal minors. Firstly, we can prove identity (164) by means of Binet-Cauchy formula.
where
The complex constant factor
here
where
where
If we define matrices
and
where
Using above identity, comparing (169), (172), (173), and (174), we find that identity (164) holds and complete the computation of D.
Secondly, we compute the most complicate determinant
with n, m = 1, 2,…, N. We thus have
The above summation obviously can be decomposed into two parts: one is extended to m1 = 0 and the other extended to m1 ≥ 1. Subtracted from (176), the part that is extended to m1 ≥ 1, the remaining parts of (176) is just C in Eq. (163) (with
which leads to
here
In the case of one simple pole and one-soliton solution as
From (167) and (168), we have (suppose
Then from (181) and (182), we attain the one-soliton solution
By further redefinition of its soliton center and initial phase, the single soliton solution can be further rewritten as usual standard form. It is easy to find, up to a permitted well-known constant global phase factor, the one-soliton solution to DNLS equation gotten in the pure Marchenko formalism is in perfectly agreement with that gotten from other approaches [23, 24, 26, 27].
As
Up to a permitted constant global phase factor, the two-soliton solution gotten above is actually equivalent to that gotten from both IST and Hirota’s method [23, 24, 26, 27], verifying the validity of the algebraic techniques that is used and our formula of the generalized multi-soliton solution. Because Marchenko equations (128), (129), (144), and (145) had been strictly proved, the multi-soliton solution is certainly right as long as we correctly use the algebraic techniques, especially Binet-Cauchy formula for the principal minor expansion of some special matrices.
Bilinear derivative operator D had been found and defined in the early 1970s by Hirota R., a Japanese mathematical scientist [30, 31, 32, 33]. Hirota’s bilinear-derivative transform (HBDT for brevity) can be used to deal with some partial differential equation and to find some special solutions, such as soliton solutions and rogue wave solutions [26, 27, 32]. In this section, we use HBDT to solve DNLS equation with VBC and search for its soliton solution. The DNLS equation with VBC, that is,
is one of the typical integrable nonlinear models, which is of a different form from the following equation:
which had been solved in Ref. [14] by using HBDT. We have paid special attention to the following solution form in it [14]:
where
here and henceforth a bar over a letter represents complex conjugation.
In view of the existing experiences of dealing with the DNLS equation, in the present section, we attempt to use the solution form (192) and HBDT to solve the DNLS equation. We demonstrate our solving approach step by step, and naturally extend our conclusion to the n-soliton case in the end.
For two differentiable functions
which is different from the usual derivative, for example,
where
for example,
➂ Suppose
Especially, we have
After a suitable solution form, for example, (192) has been selected, under the Hirota’s bilinear derivative transform, a partial differential equation like (189) can be generally changed into [20, 26, 27].
where
Substituting the above expressions (199)–(202) into Eq. (189), the latter can be reduced to [26, 27].
We can extract the needed bilinear derivative equations from Eq. (203) as follows:
Functions
Substituting (207) and (208) into (204)–(206) and equating the sum of the terms with the same orders of
The above equations, (209)–(223), contain the whole information needed to search for a soliton solution of the DNLS equation with VBC.
For the one-soliton case, due to (209)–(211) and considering the transform property ③, we can select
From (212), one can select
where the vanishing boundary condition,
Substituting (226) and (227) into Eq. (213), we can attain
From (226) and (228), we can get an expression of
Due to (224) and (229), we can also easily verify that
which immediately leads to
in Eq. (215). Then from (215), we can select
where
which is characterized with two complex parameters
Then
It is easy to find, up to a permitted constant global phase factor
On the other hand, just like in Ref. [13], we can rewrite
Here
which makes us easily extend the solution form to the case of
For the two-soliton case, again from (209), we can select
The similar procedures to that used in the one-soliton case can be used to deduce
Substituting (242) and (243) into (215), one can attain
Substituting the expressions of
Due to (243) and (244), we can also easily verify that
Then from (244), (245), (246), and (221), we can select
It can also be rewritten in a standard form as follows:
where
which is characterized with four complex parameters
we can easily transform it to a two-soliton form given in Ref. [23], up to a permitted constant global phase factor.
Generally for the case of N-soliton solution, if we select
then using an induction method, we can write the
where
therein
Here, we have some discussion in order. Because what concerns us only is the soliton solutions, our soliton solution of DNLS equation with VBC is only a subset of the whole solution set. Actually in the whole process of deriving the bilinear-form equations and searching for the one and two-soliton solutions, some of the latter results are only the sufficient but not the necessary conditions of the former equations. Thereby some possible modes might have been missing. For example, the solutions of Eqs. (209)–(211) are not as unique as in (224) and (225), some other possibilities thus get lost here. This is also why we use a term “select” to determine a solution of an equation. In another word, we have selected a soliton solution. Meanwhile, we have demonstrated in Figures 2 and 3, the three-dimensional evolution of the one- and two-soliton amplitude with time and space, respectively. The elastic collision of two solitons in the two-soliton case has been demonstrated in Figure 4(a–d) too. It can be found that each soliton keeps the same form and characteristic after the collision as that before the collision. In this section, by means of introducing HBDT and employing an appropriate solution form (192), we successfully solve the derivative nonlinear Schrödinger equation with VBC. The one- and two-soliton solutions are derived and their equivalence to the existing results is manifested. The N-soliton solution has been given by an induction method. On the other hand, by using simple parameter transformations (e.g., (235) and (252)), the soliton solutions attained here can be changed into or equivalent to that gotten based on IST, up to a permitted global constant phase factor. This section impresses us so greatly for a fact that, ranked with the extensively used IST [23] and other methods, the HBDT is another effective and important tool to deal with a partial differential equation. It is especially suitable for some integrable nonlinear models.
The evolution of one-soliton solution with time and space under parameter Λ1=−1+0.2i,η10=1 in (234).
The evolution of two-soliton solution with time and space under parameter Λ1=1+0.3i,Λ2=1−0.3i,η10=η20=1 in (251).
The elastic collision between two solitons at 4 typical moments: (a) t = −10(normalized time); (b) t = −1; \t(c) t = 1; (d) t = 10, from −10 before collision to 10 after collision.
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She performed research in perioperative autotransfusion and obtained the degree of PhD in 1993 publishing Peri-operative autotransfusion by means of a blood cell separator.\nBlood transfusion had her special interest being the president of the Haemovigilance Chamber TRIP and performing several tasks in local and national blood bank and anticoagulant-blood transfusion guidelines committees. Currently, she is working as an associate professor and up till recently was the dean at the Albert Schweitzer Hospital Dordrecht. She performed (inter)national tasks as vice-president of the Concilium Anaesthesia and related committees. \nShe performed research in several fields, with over 100 publications in (inter)national journals and numerous papers on scientific conferences. \nShe received several awards and is a member of Honour of the Dutch Society of Anaesthesia.",institutionString:null,institution:{name:"Albert Schweitzer Hospital",country:{name:"Gabon"}}},{id:"83089",title:"Prof.",name:"Aaron",middleName:null,surname:"Ojule",slug:"aaron-ojule",fullName:"Aaron Ojule",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Port Harcourt",country:{name:"Nigeria"}}},{id:"295748",title:"Mr.",name:"Abayomi",middleName:null,surname:"Modupe",slug:"abayomi-modupe",fullName:"Abayomi Modupe",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:null,institutionString:null,institution:{name:"Landmark University",country:{name:"Nigeria"}}},{id:"94191",title:"Prof.",name:"Abbas",middleName:null,surname:"Moustafa",slug:"abbas-moustafa",fullName:"Abbas Moustafa",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/94191/images/96_n.jpg",biography:"Prof. Moustafa got his doctoral degree in earthquake engineering and structural safety from Indian Institute of Science in 2002. He is currently an associate professor at Department of Civil Engineering, Minia University, Egypt and the chairman of Department of Civil Engineering, High Institute of Engineering and Technology, Giza, Egypt. He is also a consultant engineer and head of structural group at Hamza Associates, Giza, Egypt. Dr. Moustafa was a senior research associate at Vanderbilt University and a JSPS fellow at Kyoto and Nagasaki Universities. He has more than 40 research papers published in international journals and conferences. He acts as an editorial board member and a reviewer for several regional and international journals. His research interest includes earthquake engineering, seismic design, nonlinear dynamics, random vibration, structural reliability, structural health monitoring and uncertainty modeling.",institutionString:null,institution:{name:"Minia University",country:{name:"Egypt"}}},{id:"84562",title:"Dr.",name:"Abbyssinia",middleName:null,surname:"Mushunje",slug:"abbyssinia-mushunje",fullName:"Abbyssinia Mushunje",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Fort Hare",country:{name:"South Africa"}}},{id:"202206",title:"Associate Prof.",name:"Abd Elmoniem",middleName:"Ahmed",surname:"Elzain",slug:"abd-elmoniem-elzain",fullName:"Abd Elmoniem Elzain",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Kassala University",country:{name:"Sudan"}}},{id:"98127",title:"Dr.",name:"Abdallah",middleName:null,surname:"Handoura",slug:"abdallah-handoura",fullName:"Abdallah Handoura",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"École Supérieure des Télécommunications",country:{name:"Morocco"}}},{id:"91404",title:"Prof.",name:"Abdecharif",middleName:null,surname:"Boumaza",slug:"abdecharif-boumaza",fullName:"Abdecharif Boumaza",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Abbès Laghrour University of Khenchela",country:{name:"Algeria"}}},{id:"105795",title:"Prof.",name:"Abdel Ghani",middleName:null,surname:"Aissaoui",slug:"abdel-ghani-aissaoui",fullName:"Abdel Ghani Aissaoui",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/105795/images/system/105795.jpeg",biography:"Abdel Ghani AISSAOUI is a Full Professor of electrical engineering at University of Bechar (ALGERIA). He was born in 1969 in Naama, Algeria. He received his BS degree in 1993, the MS degree in 1997, the PhD degree in 2007 from the Electrical Engineering Institute of Djilali Liabes University of Sidi Bel Abbes (ALGERIA). He is an active member of IRECOM (Interaction Réseaux Electriques - COnvertisseurs Machines) Laboratory and IEEE senior member. He is an editor member for many international journals (IJET, RSE, MER, IJECE, etc.), he serves as a reviewer in international journals (IJAC, ECPS, COMPEL, etc.). He serves as member in technical committee (TPC) and reviewer in international conferences (CHUSER 2011, SHUSER 2012, PECON 2012, SAI 2013, SCSE2013, SDM2014, SEB2014, PEMC2014, PEAM2014, SEB (2014, 2015), ICRERA (2015, 2016, 2017, 2018,-2019), etc.). His current research interest includes power electronics, control of electrical machines, artificial intelligence and Renewable energies.",institutionString:"University of Béchar",institution:{name:"University of Béchar",country:{name:"Algeria"}}},{id:"99749",title:"Dr.",name:"Abdel Hafid",middleName:null,surname:"Essadki",slug:"abdel-hafid-essadki",fullName:"Abdel Hafid Essadki",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"École Nationale Supérieure de Technologie",country:{name:"Algeria"}}},{id:"101208",title:"Prof.",name:"Abdel Karim",middleName:"Mohamad",surname:"El Hemaly",slug:"abdel-karim-el-hemaly",fullName:"Abdel Karim El Hemaly",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/101208/images/733_n.jpg",biography:"OBGYN.net Editorial Advisor Urogynecology.\nAbdel Karim M. A. El-Hemaly, MRCOG, FRCS � Egypt.\n \nAbdel Karim M. A. El-Hemaly\nProfessor OB/GYN & Urogynecology\nFaculty of medicine, Al-Azhar University \nPersonal Information: \nMarried with two children\nWife: Professor Laila A. Moussa MD.\nSons: Mohamad A. M. El-Hemaly Jr. MD. Died March 25-2007\nMostafa A. M. El-Hemaly, Computer Scientist working at Microsoft Seatle, USA. \nQualifications: \n1.\tM.B.-Bch Cairo Univ. June 1963. \n2.\tDiploma Ob./Gyn. Cairo Univ. April 1966. \n3.\tDiploma Surgery Cairo Univ. Oct. 1966. \n4.\tMRCOG London Feb. 1975. \n5.\tF.R.C.S. Glasgow June 1976. \n6.\tPopulation Study Johns Hopkins 1981. \n7.\tGyn. Oncology Johns Hopkins 1983. \n8.\tAdvanced Laparoscopic Surgery, with Prof. Paulson, Alexandria, Virginia USA 1993. \nSocieties & Associations: \n1.\t Member of the Royal College of Ob./Gyn. London. \n2.\tFellow of the Royal College of Surgeons Glasgow UK. \n3.\tMember of the advisory board on urogyn. FIGO. \n4.\tMember of the New York Academy of Sciences. \n5.\tMember of the American Association for the Advancement of Science. \n6.\tFeatured in �Who is Who in the World� from the 16th edition to the 20th edition. \n7.\tFeatured in �Who is Who in Science and Engineering� in the 7th edition. \n8.\tMember of the Egyptian Fertility & Sterility Society. \n9.\tMember of the Egyptian Society of Ob./Gyn. \n10.\tMember of the Egyptian Society of Urogyn. \n\nScientific Publications & Communications:\n1- Abdel Karim M. El Hemaly*, Ibrahim M. Kandil, Asim Kurjak, Ahmad G. Serour, Laila A. S. Mousa, Amr M. Zaied, Khalid Z. El Sheikha. \nImaging the Internal Urethral Sphincter and the Vagina in Normal Women and Women Suffering from Stress Urinary Incontinence and Vaginal Prolapse. Gynaecologia Et Perinatologia, Vol18, No 4; 169-286 October-December 2009.\n2- Abdel Karim M. El Hemaly*, Laila A. S. Mousa Ibrahim M. Kandil, Fatma S. El Sokkary, Ahmad G. Serour, Hossam Hussein.\nFecal Incontinence, A Novel Concept: The Role of the internal Anal sphincter (IAS) in defecation and fecal incontinence. Gynaecologia Et Perinatologia, Vol19, No 2; 79-85 April -June 2010.\n3- Abdel Karim M. El Hemaly*, Laila A. S. Mousa Ibrahim M. Kandil, Fatma S. El Sokkary, Ahmad G. Serour, Hossam Hussein.\nSurgical Treatment of Stress Urinary Incontinence, Fecal Incontinence and Vaginal Prolapse By A Novel Operation \n"Urethro-Ano-Vaginoplasty"\n Gynaecologia Et Perinatologia, Vol19, No 3; 129-188 July-September 2010.\n4- Abdel Karim M. El Hemaly*, Ibrahim M. Kandil, Laila A. S. Mousa and Mohamad A.K.M.El Hemaly.\nUrethro-vaginoplasty, an innovated operation for the treatment of: Stress Urinary Incontinence (SUI), Detursor Overactivity (DO), Mixed Urinary Incontinence and Anterior Vaginal Wall Descent. \nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/ urethro-vaginoplasty_01\n\n5- Abdel Karim M. El Hemaly, Ibrahim M Kandil, Mohamed M. Radwan.\n Urethro-raphy a new technique for surgical management of Stress Urinary Incontinence.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/\nnew-tech-urethro\n\n6- Abdel Karim M. El Hemaly, Ibrahim M Kandil, Mohamad A. Rizk, Nabil Abdel Maksoud H., Mohamad M. Radwan, Khalid Z. El Shieka, Mohamad A. K. M. El Hemaly, and Ahmad T. El Saban.\nUrethro-raphy The New Operation for the treatment of stress urinary incontinence, SUI, detrusor instability, DI, and mixed-type of urinary incontinence; short and long term results. \nhttp://www.obgyn.net/urogyn/urogyn.asp?page=urogyn/articles/\nurethroraphy-09280\n\n7-Abdel Karim M. El Hemaly, Ibrahim M Kandil, and Bahaa E. El Mohamady. Menopause, and Voiding troubles. \nhttp://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly03/el-hemaly03-ss\n\n8-El Hemaly AKMA, Mousa L.A. Micturition and Urinary\tContinence. Int J Gynecol Obstet 1996; 42: 291-2. \n\n9-Abdel Karim M. El Hemaly.\n Urinary incontinence in gynecology, a review article.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/abs-urinary_incotinence_gyn_ehemaly \n\n10-El Hemaly AKMA. Nocturnal Enuresis: Pathogenesis and Treatment. \nInt Urogynecol J Pelvic Floor Dysfunct 1998;9: 129-31.\n \n11-El Hemaly AKMA, Mousa L.A.E. Stress Urinary Incontinence, a New Concept. Eur J Obstet Gynecol Reprod Biol 1996; 68: 129-35. \n\n12- El Hemaly AKMA, Kandil I. M. Stress Urinary Incontinence SUI facts and fiction. Is SUI a puzzle?! http://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly/el-hemaly-ss\n\n13-Abdel Karim El Hemaly, Nabil Abdel Maksoud, Laila A. Mousa, Ibrahim M. Kandil, Asem Anwar, M.A.K El Hemaly and Bahaa E. El Mohamady. \nEvidence based Facts on the Pathogenesis and Management of SUI. http://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly02/el-hemaly02-ss\n\n14- Abdel Karim M. El Hemaly*, Ibrahim M. Kandil, Mohamad A. Rizk and Mohamad A.K.M.El Hemaly.\n Urethro-plasty, a Novel Operation based on a New Concept, for the Treatment of Stress Urinary Incontinence, S.U.I., Detrusor Instability, D.I., and Mixed-type of Urinary Incontinence.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/urethro-plasty_01\n\n15-Ibrahim M. Kandil, Abdel Karim M. El Hemaly, Mohamad M. Radwan: Ultrasonic Assessment of the Internal Urethral Sphincter in Stress Urinary Incontinence. The Internet Journal of Gynecology and Obstetrics. 2003. Volume 2 Number 1. \n\n\n16-Abdel Karim M. El Hemaly. Nocturnal Enureses: A Novel Concept on its pathogenesis and Treatment.\nhttp://www.obgyn.net/urogynecolgy/?page=articles/nocturnal_enuresis\n\n17- Abdel Karim M. El Hemaly. Nocturnal Enureses: An Update on the pathogenesis and Treatment.\nhttp://www.obgyn.net/urogynecology/?page=/ENHLIDH/PUBD/FEATURES/\nPresentations/ Nocturnal_Enuresis/nocturnal_enuresis\n\n18-Maternal Mortality in Egypt, a cry for help and attention. The Second International Conference of the African Society of Organization & Gestosis, 1998, 3rd Annual International Conference of Ob/Gyn Department � Sohag Faculty of Medicine University. Feb. 11-13. Luxor, Egypt. \n19-Postmenopausal Osteprosis. The 2nd annual conference of Health Insurance Organization on Family Planning and its role in primary health care. Zagaziz, Egypt, February 26-27, 1997, Center of Complementary Services for Maternity and childhood care. \n20-Laparoscopic Assisted vaginal hysterectomy. 10th International Annual Congress Modern Trends in Reproductive Techniques 23-24 March 1995. Alexandria, Egypt. \n21-Immunological Studies in Pre-eclamptic Toxaemia. Proceedings of 10th Annual Ain Shams Medical Congress. Cairo, Egypt, March 6-10, 1987. \n22-Socio-demographic factorse affecting acceptability of the long-acting contraceptive injections in a rural Egyptian community. Journal of Biosocial Science 29:305, 1987. \n23-Plasma fibronectin levels hypertension during pregnancy. The Journal of the Egypt. Soc. of Ob./Gyn. 13:1, 17-21, Jan. 1987. \n24-Effect of smoking on pregnancy. Journal of Egypt. Soc. of Ob./Gyn. 12:3, 111-121, Sept 1986. \n25-Socio-demographic aspects of nausea and vomiting in early pregnancy. Journal of the Egypt. Soc. of Ob./Gyn. 12:3, 35-42, Sept. 1986. \n26-Effect of intrapartum oxygen inhalation on maternofetal blood gases and pH. Journal of the Egypt. Soc. of Ob./Gyn. 12:3, 57-64, Sept. 1986. \n27-The effect of severe pre-eclampsia on serum transaminases. The Egypt. J. Med. Sci. 7(2): 479-485, 1986. \n28-A study of placental immunoreceptors in pre-eclampsia. The Egypt. J. Med. Sci. 7(2): 211-216, 1986. \n29-Serum human placental lactogen (hpl) in normal, toxaemic and diabetic pregnant women, during pregnancy and its relation to the outcome of pregnancy. Journal of the Egypt. Soc. of Ob./Gyn. 12:2, 11-23, May 1986. \n30-Pregnancy specific B1 Glycoprotein and free estriol in the serum of normal, toxaemic and diabetic pregnant women during pregnancy and after delivery. Journal of the Egypt. Soc. of Ob./Gyn. 12:1, 63-70, Jan. 1986. Also was accepted and presented at Xith World Congress of Gynecology and Obstetrics, Berlin (West), September 15-20, 1985. \n31-Pregnancy and labor in women over the age of forty years. Accepted and presented at Al-Azhar International Medical Conference, Cairo 28-31 Dec. 1985. \n32-Effect of Copper T intra-uterine device on cervico-vaginal flora. Int. J. Gynaecol. Obstet. 23:2, 153-156, April 1985. \n33-Factors affecting the occurrence of post-Caesarean section febrile morbidity. Population Sciences, 6, 139-149, 1985. \n34-Pre-eclamptic toxaemia and its relation to H.L.A. system. Population Sciences, 6, 131-139, 1985. \n35-The menstrual pattern and occurrence of pregnancy one year after discontinuation of Depo-medroxy progesterone acetate as a postpartum contraceptive. Population Sciences, 6, 105-111, 1985. \n36-The menstrual pattern and side effects of Depo-medroxy progesterone acetate as postpartum contraceptive. Population Sciences, 6, 97-105, 1985. \n37-Actinomyces in the vaginas of women with and without intrauterine contraceptive devices. Population Sciences, 6, 77-85, 1985. \n38-Comparative efficacy of ibuprofen and etamsylate in the treatment of I.U.D. menorrhagia. Population Sciences, 6, 63-77, 1985. \n39-Changes in cervical mucus copper and zinc in women using I.U.D.�s. Population Sciences, 6, 35-41, 1985. \n40-Histochemical study of the endometrium of infertile women. Egypt. J. Histol. 8(1) 63-66, 1985. \n41-Genital flora in pre- and post-menopausal women. Egypt. J. Med. Sci. 4(2), 165-172, 1983. \n42-Evaluation of the vaginal rugae and thickness in 8 different groups. Journal of the Egypt. Soc. of Ob./Gyn. 9:2, 101-114, May 1983. \n43-The effect of menopausal status and conjugated oestrogen therapy on serum cholesterol, triglycerides and electrophoretic lipoprotein patterns. Al-Azhar Medical Journal, 12:2, 113-119, April 1983. \n44-Laparoscopic ventrosuspension: A New Technique. Int. J. Gynaecol. Obstet., 20, 129-31, 1982. \n45-The laparoscope: A useful diagnostic tool in general surgery. Al-Azhar Medical Journal, 11:4, 397-401, Oct. 1982. \n46-The value of the laparoscope in the diagnosis of polycystic ovary. Al-Azhar Medical Journal, 11:2, 153-159, April 1982. \n47-An anaesthetic approach to the management of eclampsia. Ain Shams Medical Journal, accepted for publication 1981. \n48-Laparoscopy on patients with previous lower abdominal surgery. Fertility management edited by E. Osman and M. Wahba 1981. \n49-Heart diseases with pregnancy. Population Sciences, 11, 121-130, 1981. \n50-A study of the biosocial factors affecting perinatal mortality in an Egyptian maternity hospital. Population Sciences, 6, 71-90, 1981. \n51-Pregnancy Wastage. Journal of the Egypt. Soc. of Ob./Gyn. 11:3, 57-67, Sept. 1980. \n52-Analysis of maternal deaths in Egyptian maternity hospitals. Population Sciences, 1, 59-65, 1979. \nArticles published on OBGYN.net: \n1- Abdel Karim M. El Hemaly*, Ibrahim M. Kandil, Laila A. S. Mousa and Mohamad A.K.M.El Hemaly.\nUrethro-vaginoplasty, an innovated operation for the treatment of: Stress Urinary Incontinence (SUI), Detursor Overactivity (DO), Mixed Urinary Incontinence and Anterior Vaginal Wall Descent. \nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/ urethro-vaginoplasty_01\n\n2- Abdel Karim M. El Hemaly, Ibrahim M Kandil, Mohamed M. Radwan.\n Urethro-raphy a new technique for surgical management of Stress Urinary Incontinence.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/\nnew-tech-urethro\n\n3- Abdel Karim M. El Hemaly, Ibrahim M Kandil, Mohamad A. Rizk, Nabil Abdel Maksoud H., Mohamad M. Radwan, Khalid Z. El Shieka, Mohamad A. K. M. El Hemaly, and Ahmad T. El Saban.\nUrethro-raphy The New Operation for the treatment of stress urinary incontinence, SUI, detrusor instability, DI, and mixed-type of urinary incontinence; short and long term results. \nhttp://www.obgyn.net/urogyn/urogyn.asp?page=urogyn/articles/\nurethroraphy-09280\n\n4-Abdel Karim M. El Hemaly, Ibrahim M Kandil, and Bahaa E. El Mohamady. Menopause, and Voiding troubles. \nhttp://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly03/el-hemaly03-ss\n\n5-El Hemaly AKMA, Mousa L.A. Micturition and Urinary\tContinence. Int J Gynecol Obstet 1996; 42: 291-2. \n\n6-Abdel Karim M. El Hemaly.\n Urinary incontinence in gynecology, a review article.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/abs-urinary_incotinence_gyn_ehemaly \n\n7-El Hemaly AKMA. Nocturnal Enuresis: Pathogenesis and Treatment. \nInt Urogynecol J Pelvic Floor Dysfunct 1998;9: 129-31.\n \n8-El Hemaly AKMA, Mousa L.A.E. Stress Urinary Incontinence, a New Concept. Eur J Obstet Gynecol Reprod Biol 1996; 68: 129-35. \n\n9- El Hemaly AKMA, Kandil I. M. Stress Urinary Incontinence SUI facts and fiction. Is SUI a puzzle?! http://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly/el-hemaly-ss\n\n10-Abdel Karim El Hemaly, Nabil Abdel Maksoud, Laila A. Mousa, Ibrahim M. Kandil, Asem Anwar, M.A.K El Hemaly and Bahaa E. El Mohamady. \nEvidence based Facts on the Pathogenesis and Management of SUI. http://www.obgyn.net/displayppt.asp?page=/English/pubs/features/presentations/El-Hemaly02/el-hemaly02-ss\n\n11- Abdel Karim M. El Hemaly*, Ibrahim M. Kandil, Mohamad A. Rizk and Mohamad A.K.M.El Hemaly.\n Urethro-plasty, a Novel Operation based on a New Concept, for the Treatment of Stress Urinary Incontinence, S.U.I., Detrusor Instability, D.I., and Mixed-type of Urinary Incontinence.\nhttp://www.obgyn.net/urogyn/urogyn.asp?page=/urogyn/articles/urethro-plasty_01\n\n12-Ibrahim M. Kandil, Abdel Karim M. El Hemaly, Mohamad M. Radwan: Ultrasonic Assessment of the Internal Urethral Sphincter in Stress Urinary Incontinence. The Internet Journal of Gynecology and Obstetrics. 2003. Volume 2 Number 1. \n\n13-Abdel Karim M. El Hemaly. Nocturnal Enureses: A Novel Concept on its pathogenesis and Treatment.\nhttp://www.obgyn.net/urogynecolgy/?page=articles/nocturnal_enuresis\n\n14- Abdel Karim M. El Hemaly. Nocturnal Enureses: An Update on the pathogenesis and Treatment.\nhttp://www.obgyn.net/urogynecology/?page=/ENHLIDH/PUBD/FEATURES/\nPresentations/ Nocturnal_Enuresis/nocturnal_enuresis",institutionString:null,institution:{name:"Al Azhar University",country:{name:"Egypt"}}},{id:"113313",title:"Dr.",name:"Abdel-Aal",middleName:null,surname:"Mantawy",slug:"abdel-aal-mantawy",fullName:"Abdel-Aal Mantawy",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Ain Shams University",country:{name:"Egypt"}}}],filtersByRegion:[{group:"region",caption:"North America",value:1,count:5681},{group:"region",caption:"Middle and South America",value:2,count:5161},{group:"region",caption:"Africa",value:3,count:1683},{group:"region",caption:"Asia",value:4,count:10200},{group:"region",caption:"Australia and Oceania",value:5,count:886},{group:"region",caption:"Europe",value:6,count:15610}],offset:12,limit:12,total:1683},chapterEmbeded:{data:{}},editorApplication:{success:null,errors:{}},ofsBooks:{filterParams:{hasNoEditors:"0",sort:"dateEndThirdStepPublish"},books:[{type:"book",id:"10542",title:"Molecular Epidemiology Study of Mycobacterium Tuberculosis Complex",subtitle:null,isOpenForSubmission:!0,hash:"29279e34f971687dc28de62534335ac4",slug:null,bookSignature:"Ph.D. Yogendra Shah",coverURL:"https://cdn.intechopen.com/books/images_new/10542.jpg",editedByType:null,editors:[{id:"278914",title:"Ph.D.",name:"Yogendra",surname:"Shah",slug:"yogendra-shah",fullName:"Yogendra Shah"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10552",title:"Montmorillonite",subtitle:null,isOpenForSubmission:!0,hash:"c4a279761f0bb046af95ecd32ab09e51",slug:null,bookSignature:"Prof. Faheem Uddin",coverURL:"https://cdn.intechopen.com/books/images_new/10552.jpg",editedByType:null,editors:[{id:"228107",title:"Prof.",name:"Faheem",surname:"Uddin",slug:"faheem-uddin",fullName:"Faheem Uddin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10281",title:"Nanopores",subtitle:null,isOpenForSubmission:!0,hash:"73c465d2d70f8deca04b05d7ecae26c4",slug:null,bookSignature:"Dr. Sadia Ameen, Dr. M. 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