Superposed Hyperbolic Kink and Pulse Solutions of Coupled $\phi^4$, NLS and MKdV Equations

TL;DR

This paper presents new superposed hyperbolic kink and pulse solutions for coupled nonlinear equations, demonstrating that superposition principles extend beyond linear systems to complex coupled models like $\, ext{phi}^4$, NLS, and MKdV equations.

Contribution

It introduces a novel superposition approach for coupled nonlinear equations, expanding the understanding of solution structures in these systems.

Findings

Superposed solutions expressed as sum or difference of hyperbolic kinks or pulses.

Extension of superposition concept to coupled nonlinear equations.

Demonstration of superposition in $\, ext{phi}^4$, NLS, and MKdV models.

Abstract

We obtain novel solutions of a coupled $\phi^4$, a coupled nonlinear Schr\"odinger (NLS) and a coupled modified Korteweg de Vries (MKdV) model which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic kink or two hyperbolic pulse solutions. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.