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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212047 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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 |
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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.
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| 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 |