Note on self-adjoint sub-classes of fourth-order evolution equations with time dependent coefficients

TL;DR

This paper classifies self-adjoint sub-classes of fourth-order nonlinear evolution equations with time-dependent coefficients and derives conservation laws using a new theorem, extending recent research in the field.

Contribution

It generalizes previous classifications by including time-dependent coefficients and applies a new conservation theorem to establish related conservation laws.

Findings

Identification of self-adjoint sub-classes with time-dependent coefficients

Derivation of conservation laws for these equations

Extension of existing classifications to more general cases

Abstract

The self-adjoint sub-classes of nonlinear evolution equations of fourth-order with time dependent coefficients are determined, generalizing some recent results. Using the new conservation theorem recently proved by Nail Ibragimov some conservation laws for time dependent equations are established illustrating the main results.