The fundamental lattice solitons are explored in a nonlocal nonlinear medium with self-focusing and self-defocusing quintic nonlinearity. The band-gap boundaries, soliton profiles, and stability domains of fundamental solitons are investigated comprehensively by the linear stability spectra and nonlinear evolution of the solitons. It is demonstrated that fundamental lattice solitons can stay stable for a wide range of parameters with the weak self-focusing and self-defocusing quintic nonlinearity, while strong self-focusing and self-defocusing quintic nonlinearities are shortened the propagation distance of evolved solitons. Furthermore, it is observed that when the instability emerges from strong quintic nonlinearity, increasing anisotropy of the medium and modification of lattice depth can be considered as a collapse arrest mechanism.
Part of the book: The Nonlinear Schrödinger Equation
Stability dynamics of dipole solitons have been numerically investigated in a nonlocal nonlinear medium with self-focusing and self-defocusing quintic nonlinearity by the squared-operator method. It has been demonstrated that solitons can stay nonlinearly stable for a wide range of each parameter, and two nonlinearly stable regions have been found for dipole solitons in the gap domain. Moreover, it has been observed that instability of dipole solitons can be improved or suppressed by modification of the potential depth and strong anisotropy coefficient.
Part of the book: Vortex Dynamics