Chapters authored
Soliton and Rogue-Wave Solutions of Derivative Nonlinear Schrödinger Equation - Part 1
Based upon different methods such as a newly revised version of inverse scattering transform, Marchenko formalism, and Hirota’s bilinear derivative transform, this chapter aims to study and solve the derivative nonlinear Schrödinger (DNLS for brevity) equation under vanishing boundary condition (VBC for brevity). The explicit one-soliton and multi-soliton solutions had been derived by some algebra techniques for the VBC case. Meanwhile, the asymptotic behaviors of those multi-soliton solutions had been analyzed and discussed in detail.
Part of the book: Nonlinear Optics
Soliton and Rogue-Wave Solutions of Derivative Nonlinear Schrödinger Equation - Part 2
A revised and rigorously proved inverse scattering transform (IST for brevity) for DNLS+ equation, with a constant nonvanishing boundary condition (NVBC) and normal group velocity dispersion, is proposed by introducing a suitable affine parameter in the Zakharov-Shabat IST integral; the explicit breather-type and pure N-soliton solutions had been derived by some algebra techniques. On the other hand, DNLS equation with a non-vanishing background of harmonic plane wave is also solved by means of Hirota’s bilinear formalism. Its space periodic solutions are determined, and its rogue wave solution is derived as a long-wave limit of this space periodic solution.
Part of the book: Nonlinear Optics