Approximate symmetries, conservation laws and numerical solutions for a class of perturbed linear wave type system

Abstract

The present work considers the Lie group analysis of a system of linear wave type perturbed systems. The methodology is based on finding approximate symmetry operators of a given system. Approximate conservation laws are found via an approximate version of Noether’s theorem. This is based on the modified Noether’s method provided by Ibragimov. Finally a numerical method is applied to solve the considered system.

Key words: Approximate symmetry, approximate conservation laws, Noether’s theorem, non-linear self-adjointness, Legendre polynomials.