Discovering optical solutions to a nonlinear Schrödinger equation and its bifurcation and chaos analysis

Abstract

Abstract The pursuit of solitary wave solutions to complex nonlinear partial differential equations is gaining significance across various disciplines of nonlinear science. This study seeks to uncover the solutions to the perturbed nonlinear Schrödinger equation using a robust and efficient analytical method, namely, the generalized exponential rational function technique. This equation is a fundamental tool used in various fields, including fluid mechanics, nonlinear optics, plasma physics, and optical communication systems, and has numerous practical applications across multiple disciplines. The employed method in this study stands out from existing approaches by being more comprehensive and straightforward. It offers a broader range of symbolic structures, surpassing the capabilities of some previously known methods. By applying this method to the perturbed nonlinear Schrödinger equation, we obtain a variety of exact solutions that significantly expand the existing literature and provide a fresh understanding of the model’s properties. Through numerical simulations, we demonstrate the dynamic characteristics of the system, including bifurcation and chaos analysis, and validate our findings by adjusting parameter settings to match expected behaviors.