Unveiling complexity: Exploring chaos and solitons in modified nonlinear Schrödinger equation

This study delves deep into the complexities of the modified nonlinear Schrodinger equation. Through the Galilean transformation, we derive a dynamic system linked to the equation. Using planar dynamical systems theory, we investigate bifurcation phenomena and introduce perturbations to reveal chaotic behaviors. Phase portraits offer visual insights, while sensitivity analysis using the Runge-Kutta method emphasizes solution stability against initial condition variations. Leveraging the planar dynamical system method, we generate diverse solitons, including periodic, bright, and dark solitons. This work enhances our grasp of intricate dynamics and their broader implications.