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TMF, 2018, Volume 195, Number 1, Pages 27–43 (Mi tmf9409)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00289_a
This research is supported by the Russian Foundation for Basic Research (Grant No. 16-01-00289_a).


DOI: https://doi.org/10.4213/tmf9409

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

Bibliographic databases:

Document Type: Article
PACS: 02.30.Ik
MSC: 37K10; 37K35
Received: 01.06.2017
Revised: 13.07.2017

Citation: V. E. Adler, “Integrable seven-point discrete equations and second-order evolution chains”, TMF, 195:1 (2018), 27–43; Theoret. and Math. Phys., 195:1 (2018), 513–528

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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