Approximate Noether Symmetries of Perturbed Lagrangians and Approximate Conservation Laws

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.

Keywords

• approximate Lie symmetries
• perturbed Lagrangians
• approximate Noether theorem
• approximate conservation laws