On conversion of high-frequency soliton solutions to a (1+1)-dimensional nonlinear evolution equation

TL;DR

This paper derives a (1+1)-dimensional nonlinear evolution equation modeling high-frequency perturbations in relaxing media, revealing three solution types based on dissipation levels.

Contribution

The paper introduces a new nonlinear evolution equation specifically designed for high-frequency perturbations in relaxing media, expanding understanding of such systems.

Findings

Equation admits three solution types depending on dissipative parameter

Provides a mathematical framework for high-frequency wave propagation in relaxing media

Enhances modeling capabilities for nonlinear wave phenomena

Abstract

We derive a (1+1)-dimensional nonlinear evolution equation (NLE) which may model the propagation of high-frequency perturbations in a relaxing medium. As a result, this equation may possess three typical solutions depending on a dissipative parameter.