Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

Abstract

In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.