Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Abstract

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.

arXiv comment27 pages

References in corpus (9)

• Classification of integrable equations on quad-graphs. The consistency approach
• Algebraic entropy
• Discrete analogues of the Liouville equation
• Integrable lattice equations and their growth properties
• Searching for integrable lattice maps using factorization
• Second order integrability conditions for difference equations. An integrable equation
• Discrete time Bogoyavlensky lattices
• Integrable 7-point discrete equations and evolution lattice equations of order 2
• An unusual series of autonomous discrete integrable equations on the square lattice

Cited by in corpus (5)

• Perturbative Symmetry Approach for Differential-Difference Equations
• An unusual series of autonomous discrete integrable equations on the square lattice
• Algebraic entropy for systems of quad equations
• Linear relations for Laurent polynomials and lattice equations
• Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries