Dynamic behavior and modulation instability for a generalized nonlinear Schrödinger equation with nonlocal nonlinearity

Abstract

This paper focus on the generalized nonlinear Schrödinger equation with triple refractive index and
nonlocal nonlinearity, which is used to describe the evolution state of optical solitons in fiber optic
propagation. Firstly, the complex exponential traveling wave transformation and substitution method
are utilized to convert the equation into two-dimensional planar dynamic system, and then by phase
portrait the developmental patterns of solutions are qualitatively analyzing. Meanwhile, the evolution
of solutions under different disturbances in the system is discussed. Qualitative analysis of the system
are displayed through Poincar´ e section and sensitivity analysis. Finally, the instability of the system is
modulated by using linear stability analysis method, and the corresponding conditions for steady-state
solutions and the gain spectrum function are obtained.