Conditional Symmetry and Reductions for the Two-Dimensional Nonlinear Wave Equation. I. General Case

TL;DR

This paper classifies Q-conditional symmetries for two-dimensional nonlinear wave equations and discusses the reductions associated with these symmetries, providing a systematic approach to simplifying and solving such equations.

Contribution

It offers a comprehensive classification of inequivalent reductions based on nonlinear symmetries, advancing the understanding of wave equation solutions.

Findings

Classification of Q-conditional symmetries achieved

Identification of inequivalent reductions for the wave equations

Framework for applying symmetries to simplify nonlinear wave equations

Abstract

We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.