Classification of five-point differential-difference equations

Abstract

Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the discrete Sawada-Kotera equations. The resulting list contains 17 equations some of which seem to be new. We have found non-point transformations relating most of the resulting equations among themselves and their generalized symmetries.

29 pages

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Cited by in corpus (13)

• Classification of five-point differential-difference equations II
• Perturbative Symmetry Approach for Differential-Difference Equations
• Integrable 7-point discrete equations and evolution lattice equations of order 2
• An unusual series of autonomous discrete integrable equations on the square lattice
• On the integrability of a discrete analogue of the Kaup-Kupershmidt equation
• Algebraic entropy of a class of five-point differential-difference equations
• Transformations, symmetries and Noether theorems for differential-difference equations
• Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
• Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
• Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations
• Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation
• Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries
• On the integrability of a lattice equation with two continuum limits