This article is cited in 6 papers

Integrable seven-point discrete equations and second-order evolution chains

V. E. Adler

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

Abstract: We consider differential–difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a second-order scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Keywords: integrability, discrete equation, differential–difference equation, lattice, symmetry.

PACS: 02.30.Ik

MSC: 37K10; 37K35

Received: 01.06.2017
Revised: 13.07.2017

DOI: 10.4213/tmf9409

 English version: Theoretical and Mathematical Physics, 2018, 195:1, 513–528

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