Lie group classification and conservation laws of a class of hyperbolic equations

TL;DR

This paper introduces a new systematic method for classifying symmetries of hyperbolic differential equations and computes conservation laws for physically relevant cases, enhancing understanding of their integrability.

Contribution

It proposes a novel approach for Lie group classification based on linear dependence analysis, applied to a family of hyperbolic equations with physical significance.

Findings

New classification method for hyperbolic equations

Conservation laws for key equations in the family

Insights into symmetry integrability of the equations

Abstract

A new method for the Lie group classification of differential equations is proposed. It is based of the determination of all possible cases of linear dependence of certain indeterminate appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the said family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.