Bifurcation Analysis, Sensitivity Analysis, and Jacobi Elliptic Function Structures to a Generalized Nonlinear Schrödinger Equation

The present paper provides an investigation into the propagation of soliton waves for a generalized nonlinear Schrödinger (gNLS) equation. To this end, the bifurcation analysis (BA) of the dynamical system (DS) is first conducted through utilizing the dynamical system theory (DST). Through the Runge–Kutta (RK) scheme, the sensitivity analysis (SA) is then examined to make sure that small variations in seed values do not have a noticeable impact on the stability of the solution. In the end, the dynamical system approach is applied to derive a family of Jacobi elliptic waves of the gNLS equation. Some case studies are given to examine the influence of the Kerr law in the propagation of bright and dark solitons.