Invariant soliton solutions for the coupled nonlinear Schrodinger type equation

The Schrodinger equation is an essential model in quantum mechanics. It simulates fas-cinating 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 Schrodinger equations using the Lie classical approach combined with modified (G'/G)-expansion method and polynomial type assump-tion. 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 con-clude that the current methods are effective, powerful, and provide simple, trustworthy solutions. Maple software was used to check all of the obtained solutions.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

This study investigates the optical soliton solutions of nonlinear triple-component Schrodinger equations using the Lie classical approach combined with modified (G'/G)-expansion method and polynomial type assumption. Several explicit solutions including hyperbolic, periodic, and power series solutions are obtained. The stability of one of the reductions is also examined using phase plane theory. Maple software is utilized for graphical representation and verification of the obtained solitons.