Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations

TL;DR

This paper explores methods to reduce complex multidimensional wave equations to simpler two-dimensional forms, uncovering new symmetries and equivalence classes to facilitate their analysis.

Contribution

It systematically investigates Lie and non-classical reductions of multidimensional wave equations, revealing new conditional and hidden symmetries.

Findings

Identification of new conditional symmetries

Discovery of hidden symmetries in wave equations

Classification of reduced equations and their equivalence classes

Abstract

We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.