Classification of integrable discrete Klein-Gordon models

TL;DR

This paper applies a Lie algebraic integrability test to classify integrable Klein-Gordon equations on quad-graphs, identifying known models and discovering a new integrable example with its higher symmetry.

Contribution

It introduces a classification of integrable Klein-Gordon models on quad-graphs using Lie algebraic methods, including a new integrable example.

Findings

List of known integrable Klein-Gordon models on quad-graphs.

Identification of a new integrable Klein-Gordon model.

Higher symmetry of the new model is presented.

Abstract

The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models. A new integrable example is found, its higher symmetry is presented.