Approximate Noether symmetries of perturbed Lagrangians and approximate conservation laws

TL;DR

This paper develops a framework for identifying approximate Noether symmetries in perturbed Lagrangian systems, leading to approximate conservation laws with applications demonstrated.

Contribution

It introduces a new approach for approximate Noether symmetries in variational problems with small perturbations, extending classical symmetry methods.

Findings

Derived an approximate Noether theorem for perturbed systems.

Constructed approximate conservation laws from symmetries.

Presented applications illustrating the method's effectiveness.

Abstract

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we state an approximate Noether theorem leading to the construction of approximate conservation laws. Some illustrative applications are presented.