Classification of five-point differential-difference equations II

Abstract

Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201 (27pp)], of integrable autonomous five-point differential-difference equations. The resulting list, up to autonomous point transformations, contains 14 equations some of which seem to be new. We have found non-autonomous or non-point transformations relating most of the obtained equations among themselves as well as their generalized symmetries.

18 pages

References in corpus (4)

• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
• Classification of five-point differential-difference equations
• Integrable Möbius invariant evolutionary lattices of second order
• Non-invertible transformations for the classification of differential-difference equations

Cited by in corpus (9)

• Perturbative Symmetry Approach for Differential-Difference Equations
• An unusual series of autonomous discrete integrable equations on the square lattice
• 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
• Simplifications of Lax pairs for differential-difference equations by gauge transformations and (doubly) modified integrable equations
• Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations
• On matrix Lax representations and constructions of Miura-type transformations for differential-difference equations
• Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries