On the structure of conservation laws of (3+1)-dimensional wave equation

In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The non-local conservation theorems and multipliers approach are performed on the (3+1)-dimensional wave equation. We obtain conservation laws by using five methods, such as direct method, Noether’s method, extended Noether’s method, Ibragimov’s method; and finally we can derive infinitely many conservation laws from a known conservation law viewed as the last method. We also derive some exact solutions using some conservation laws Anco and Bluman (2002). Keywords: Wave equation, Conservation laws, Lie symmetry, Direct method, Noether’s theorem, Boyer’s formulation, Mathematics Subject Classification: 76M60, 70H33, 35J0

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

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