Integrable hyperbolic equations of sin-Gordon type

TL;DR

This paper provides a comprehensive list of nonlinear hyperbolic equations of the sin-Gordon type, highlighting their integrability properties and including both equations of this type and those linearizable by substitutions.

Contribution

It offers a complete classification of integrable hyperbolic equations with third-order symmetries, expanding understanding of sin-Gordon type equations.

Findings

List of nonlinear hyperbolic equations with integrable symmetries

Identification of equations linearizable by differential substitutions

Comprehensive classification of sin-Gordon type equations

Abstract

A complete list of nonlinear one-field hyperbolic equations having generalized integrable x- and y-symmetries of the third order is presented. The list includes both sin-Gordon type equations and equations linearizable by differential substitutions.