Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations

TL;DR

This paper investigates potential symmetries and conservation laws for generalized quasilinear hyperbolic equations using Lie group methods, partial Lagrangian approach, and focuses on physically relevant cases.

Contribution

It introduces a systematic approach to find potential symmetries and explicit invariant solutions for these equations, highlighting physically interesting scenarios.

Findings

Identified potential symmetries for specific hyperbolic equations.

Derived conservation laws using partial Lagrangian methods.

Provided explicit invariant solutions in physically relevant cases.

Abstract

Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which admit potential symmetries. Then by using the partial Lagrangian approach, we find conservation laws for this equation in three physically interesting cases.