Modulational instability, bifurcation study, sensitivity analysis, and Jacobi elliptic waves of a resonant nonlinear Schrödinger equation

Abstract

The current paper formally investigates the propagation of specific waves modeled by a resonant nonlinear Schrödinger equation (RNLSE). In particular, in-depth research is conducted on the RNLSE, which involves various effects such as Bohm potential, detuning effect, etc. The study begins with the modulational instability (MI) of the governing model and goes on with its bifurcation analysis (BA) using the dynamical system theory. Additionally, a sensitivity analysis (SA) is performed to ensure that minor changes in seed values do not adversely affect the solution’s stability. The paper ends with retrieving several Jacobi elliptic and soliton waves and analyzing the impact of nonlinear parameters on the dynamics of such waves. The outcomes effectively show how to control the width and amplitude of Jacobi elliptic and soliton waves.