The solutions of Nonlinear Evaluation equations via Hermite Approximation

TL;DR

This paper introduces an extension of the auxiliary equation method using Hermite differential equations to find new exact traveling wave solutions for nonlinear partial differential equations, broadening the solution space.

Contribution

It develops a novel approach by integrating Hermite equations into the auxiliary equation method for nonlinear PDEs.

Findings

Extended solution space for nonlinear PDEs

New exact traveling wave solutions obtained

Method demonstrated on specific equations

Abstract

It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations using Hermite differential equation so the solution space of nonlinear partial differential equations is extended too.