Jacobi elliptic function solutions for the resonant nonlinear Schrödinger equation with anti-cubic nonlinearity

Abstract

In this paper, the newly ϕ6-model expansion method is applied to construct families of Jacobi elliptic function solutions for the resonant nonlinear Schrödinger equation (RNLSE) with anti-cubic nonlinearity. Those solutions degenerate into hyperbolic and trigonometric solutions as the modulus approaches 1 and 0, respectively. Through this approach, we were able to successfully identify and derive a diverse type of solitons, encompassing dark, bright, kink, periodic, singular soliton, and periodic singular solitons. The findings of this study may improve the nonlinear dynamical features of the equation. Additionally, exciting graphs are used to explain and highlight the data’s dynamical properties. The results will be important in nonlinear optics, fluid dynamics, quantum physics, and other fields of science. A wider range of nonlinear partial differential equations can be handled with this newly approach.