New traveling wave solutions and dynamic behavior analysis of the nonlinear Rangwala–Rao model

Abstract

This work investigates the nonlinear Rangwala–Rao equation, which stems from the mixed derivative nonlinear Schrödinger equation. For retrieving new exact solutions to the equation, the complete discriminant system for polynomial method is employed. In results, some novel traveling wave solutions, including solitary wave solutions, triangular function solutions, periodic solutions and Jacobi elliptic function solutions are obtained and demonstrated through numerical simulations. The bifurcations of phase velocity fields are depicted to reveal the dynamic behavior of the Rangwala-Rao equation using the qualitative theory of dynamical systems. Furthermore, considering external perturbation, the chaotic motions of the perturbed Rangwala-Rao equation are investigated.

Keywords

• Rangwala–Rao equation
• Traveling wave solutions
• Complete discriminant system for polynomial method
• Qualitative analysis
• Bifurcation