Instability of modulation wave train and disturbance of time period in slightly stable media for unstable nonlinear Schrödinger dynamical equation

Abstract

In this study, we constructed the exact traveling and soliton solutions for unstable nonlinear Schrödinger equation (UNLSE) by a modified mathematical method. The UNLSE explains the disorder of a time period in slightly unstable and stable medium, and also accomplishes the instability for modulated carrier wave. The demonstrated soliton solutions represent to bright-dark solitons, periodic solitary wave, and traveling waves. This technique is more efficient and powerful to investigate various kinds of soliton solutions for higher order unstable nonlinear PDEs. By applying symbolic computations, the physical interpretations of soliton solutions represent by two- and three-dimensions graphical. Our obtained results may helpful in the study of nonlinear optics, fiber optics, solitonic dynamic, and various kinds of physical sciences.