Integrable 7-point discrete equations and evolution lattice equations of order 2

Abstract

We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution lattice equation of order 2. The general scheme is illustrated by a number of examples, including an analog of the elliptic Yamilov lattice equation.

18 pages, 2 figures

References in corpus (3)

• 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

Cited by in corpus (4)

• Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
• An unusual series of autonomous discrete integrable equations on the square lattice
• Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
• Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries