Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations

TL;DR

This paper characterizes the point and contact equivalence groupoids of a key class of two-dimensional quasilinear hyperbolic equations, revealing their structure and normalization properties.

Contribution

It establishes the normalization of the class and describes the generators of its contact equivalence groupoid, including transformations related to the wave equation.

Findings

The class is normalized with respect to point transformations.

The contact equivalence groupoid is generated by prolongations, the wave equation's vertex group, and admissible transformations.

Provides a detailed description of the structure of equivalence groupoids for these equations.

Abstract

We describe the point and contact equivalence groupoids of an important class of two-dimensional quasilinear hyperbolic equations. In particular, we prove that this class is normalized in the usual sense with respect to point transformations, and its contact equivalence groupoid is generated by the first-order prolongation of its point equivalence groupoid, the contact vertex group of the wave equation and a family of contact admissible transformations between trivially Darboux-integrable equations.