Algebraic method for finding equivalence groups

TL;DR

This paper extends an algebraic method to compute the complete equivalence group of differential equation classes, using algebraic structures like automorphisms and megaideals, with applications to nonlinear wave equations.

Contribution

It introduces two algebraic approaches for finding equivalence groups, enhancing the existing symmetry analysis techniques for differential equations.

Findings

Successfully computed the equivalence group for nonlinear wave equations

Demonstrated the effectiveness of megaideal-based method

Provided a systematic algebraic framework for equivalence group determination

Abstract

The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.