Vector hyperbolic equations on the sphere possessing integrable third order symmetries

TL;DR

This paper classifies vector hyperbolic equations on the sphere with integrable third order symmetries, introduces new integrable models, and constructs their vector Bäcklund transformations, advancing the understanding of integrable hyperbolic systems.

Contribution

It provides complete lists of integrable vector hyperbolic equations on the sphere and constructs Bäcklund transformations for these new models.

Findings

Several new integrable hyperbolic vector models identified

Explicit vector Bäcklund transformations constructed for all new equations

Classification of equations with third order symmetries achieved

Abstract

The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we mean the existence of vector Backlund transformations depending on a parameter. For all new equations such transformations are constructed.