Invariant soliton solutions for the coupled nonlinear Schrödinger type equation

Abstract

The Schrödinger equation is an essential model in quantum mechanics. It simulates fascinating nonlinear physical phenomena, such as shallow-water waves, hydrodynamics, harmonic oscillator, nonlinear optics, and quantum condensates. The purpose of this study is to look at the optical soliton solutions to nonlinear triple-component Schrödinger equations using the Lie classical approach combined with modified (G′/G)-expansion method and polynomial type assumption. As a result of these approaches, some explicit solutions such as hyperbolic, periodic, and power series solutions are found. In addition, we look at the stability of the corresponding to one of the reductions using phase plane theory. Maple software is used to graphically represent some of the acquired solitons and phase portraits. Compared to the other techniques, we can conclude that the current methods are effective, powerful, and provide simple, trustworthy solutions. Maple software was used to check all of the obtained solutions.

Keywords

• Lie classical approach
• Modified (G′/G)-expansion method
• Solitons
• Phase plane theory