Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane

Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to Yamilov's theorem. We shall apply this result to a class...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2023
Main Authors: Levi, Decio, Rodríguez, Miguel A.
Format: Article
Language:English
Published: Інститут математики НАН України 2023
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212047
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane. Decio Levi and Miguel A. Rodríguez. SIGMA 19 (2023), 084, 7 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862682323138379776
author Levi, Decio
Rodríguez, Miguel A.
author_facet Levi, Decio
Rodríguez, Miguel A.
citation_txt Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane. Decio Levi and Miguel A. Rodríguez. SIGMA 19 (2023), 084, 7 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to Yamilov's theorem. We shall apply this result to a class of differential-difference equations obtained as partial continuous limits of 3-point difference equations in the plane and conclude that they cannot be integrable.
first_indexed 2026-03-17T03:55:02Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-212047
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-17T03:55:02Z
publishDate 2023
publisher Інститут математики НАН України
record_format dspace
spelling Levi, Decio
Rodríguez, Miguel A.
2026-01-23T10:12:14Z
2023
Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane. Decio Levi and Miguel A. Rodríguez. SIGMA 19 (2023), 084, 7 pages
1815-0659
2020 Mathematics Subject Classification: 39A14; 39A36
arXiv:2304.06956
https://nasplib.isofts.kiev.ua/handle/123456789/212047
https://doi.org/10.3842/SIGMA.2023.084
Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to Yamilov's theorem. We shall apply this result to a class of differential-difference equations obtained as partial continuous limits of 3-point difference equations in the plane and conclude that they cannot be integrable.
We thank the anonymous referees for corrections, useful suggestions, and constructive criticism that helped improve this article. MAR acknowledges the support of Universidad Complutense de Madrid (Spain), under grant G/6400100/3000.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
Article
published earlier
spellingShingle Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
Levi, Decio
Rodríguez, Miguel A.
title Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
title_full Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
title_fullStr Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
title_full_unstemmed Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
title_short Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane
title_sort non-existence of s-integrable three-point partial difference equations in the lattice plane
url https://nasplib.isofts.kiev.ua/handle/123456789/212047
work_keys_str_mv AT levidecio nonexistenceofsintegrablethreepointpartialdifferenceequationsinthelatticeplane
AT rodriguezmiguela nonexistenceofsintegrablethreepointpartialdifferenceequationsinthelatticeplane