Invariance of the quasilinear equations of hiperbolic type with respect to the three-parametric Lie algebras

TL;DR

This paper classifies quasi-linear hyperbolic differential equations with two variables that are invariant under three-parameter Lie groups, providing a complete description of their symmetry properties.

Contribution

It offers a complete classification of such equations based on their invariance under three-parameter Lie groups, filling a gap in symmetry analysis.

Findings

Complete classification of invariant quasi-linear hyperbolic equations

Identification of symmetry groups for these equations

Foundation for solving or simplifying these equations using symmetry methods

Abstract

We have solved completely the problem of the description of quasi-linear hyperbolic differential equations in two independent variables that are invariant under three-parameter Lie groups.