Journal of Nonlinear Mathematical Physics

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Volume 26, Issue 3, May 2019, Pages 333 - 357

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

Authors
Rustem N. Garifullin
Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation,rustem@matem.anrb.ru
Giorgio Gubbiotti*
School of Mathematics and Statistics, F07, The University of Sydney, New South Wales 2006, Australia,giorgio.gubbiotti@sydney.edu.au
Ravil I. Yamilov
Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation,RvlYamilov@matem.anrb.ru
* Corresponding author
Corresponding Author
Giorgio Gubbiotti
Received 26 October 2018, Accepted 1 February 2019, Available Online 6 January 2021.
DOI
10.1080/14029251.2019.1613050How to use a DOI?
Keywords
Integrability; Generalized symmetries; Quad-equations
Abstract

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.

Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 3
Pages
333 - 357
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2019.1613050How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Rustem N. Garifullin
AU  - Giorgio Gubbiotti
AU  - Ravil I. Yamilov
PY  - 2021
DA  - 2021/01/06
TI  - Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 333
EP  - 357
VL  - 26
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1613050
DO  - 10.1080/14029251.2019.1613050
ID  - Garifullin2021
ER  -