Approximate nonlinear self-adjointness and approximate conservation laws

TL;DR

This paper introduces the concept of approximate nonlinear self-adjointness for perturbed PDEs, enabling the construction of approximate conservation laws beyond traditional methods, demonstrated through nonlinear wave equations.

Contribution

It presents a new framework for approximate nonlinear self-adjointness and develops a method to derive conservation laws not accessible by existing approaches.

Findings

New concept of approximate nonlinear self-adjointness introduced

Method to construct approximate conservation laws beyond Noether theorem

Application to perturbed nonlinear wave equations demonstrates effectiveness

Abstract

In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness.