Generalized symmetry integrability test for discrete equations on the square lattice

Abstract

We present an integrability test for discrete equations on the square lattice, which is based on the existence of a generalized symmetry. We apply this test to a number of equations obtained in different recent papers. As a result we prove the integrability of 7 equations which differ essentially from the $Q_V$ equation introduced by Viallet and thus from the Adler-Bobenko-Suris list of equations therein contained.

References in corpus (6)

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• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
• Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
• Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions
• Classification of integrable discrete Klein-Gordon models
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• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
• On the integrability of a new lattice equation found by multiple scale analysis
• Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole Transformations
• Symmetries of the Continuous and Discrete Krichever-Novikov Equation
• Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations
• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• Classification of integrable discrete Klein-Gordon models
• An unusual series of autonomous discrete integrable equations on the square lattice
• An algebraic method of classification of S-integrable discrete models
• Algebraic entropy of a class of five-point differential-difference equations
• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
• Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure