Self-adjoint sub-classes of third and fourth-order evolution equations

TL;DR

This paper identifies self-adjoint subclasses of third and fourth-order evolution equations, establishes conservation laws, and generalizes the findings to higher-order equations, contributing to the understanding of their mathematical properties.

Contribution

It introduces new self-adjoint subclasses of third and fourth-order evolution equations and extends the concept to more general higher-order cases.

Findings

Identified self-adjoint subclasses of third-order equations

Established conservation laws for these equations

Presented a generalization to fourth-order evolution equations

Abstract

In this work a class of self-adjoint quasilinear third-order evolution equations is determined. Some conservation laws of them are established and a generalization on a self-adjoint class of fourth-order evolution equations is presented.