Bright-dark solitary waves, complexitons, Guassian solitons, and traveling wave solitons of the second-order non-linear Schrödinger equation with spatial and temporal dispersion

Abstract

In this paper, we consider the non-linear Schrödinger equation in fibers with the presence of group velocity dispersion, selfphase modulation and second-order dispersion terms. Using the ansatz method, we derive its bright, dark, complexitons, Gaussian, and traveling wave solitons, respectively. Moreover, we provide the graphical analysis of some solutions in order to better understand their dynamical behavior.