Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity

Abstract

In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schr & ouml;dinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponential function combinations are applied to construct the wave solutions. The accuracy of the derived solitons is validated through symbolic computations performed in Wolfram Mathematica, accompanied by graphical visualizations of the proposed solutions. The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. Additionally, introducing perturbed terms is examined, revealing chaotic patterns in the system. The impact of variations in amplitude and frequency parameters on the system's dynamical behaviour is thoroughly investigated. The findings underscore the efficiency and reliability of the applied techniques, demonstrating their applicability to a wide range of complex nonlinear systems.