Novel Superposed Kink and Pulse Solutions for $\phi^4$, MKdV, NLS and Other Nonlinear Equations

TL;DR

This paper introduces new superposed periodic and hyperbolic kink and pulse solutions for various nonlinear equations, expanding the understanding of their solution structures in mathematical physics.

Contribution

It presents novel superposed solutions for a range of nonlinear equations, including $^4$, MKdV, NLS, and their higher-order variants, which were not previously known.

Findings

Existence of superposed periodic kink and pulse solutions

Some equations admit superposed hyperbolic kink solutions

Broad applicability across multiple nonlinear models

Abstract

We show that a number of nonlinear equations including symmetric as well as asymmetric $\phi^4$, modified Korteweg de Vries (MKdV), mixed KdV-MKdV, nonlinear Schr\"odinger (NLS), quadratic-cubic NLS as well as higher order neutral scalar field theories, higher order KdV-MKdV and higher order quadratic-cubic NLS admit superposed periodic kink and pulse solutions and some of them also admit superposed hyperbolic kink solutions.