Potential Symmetries and Conservation Laws for p.d.e.s including Perturbations

Abstract

Relationships between symmetries and conservation laws of perturbed partial differential equations are reviewed. Potential symmetries and their applications to perturbed partial differential equations and conservation laws are presented in detail. An example of a perturbed wave equation for an inhomogeneous medium is solved in detail. Proofs of some of the lesser-known theorems are outlined. A wide range of examples is given to further explain these concepts.