A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms
We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms w...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
| ISSN: | 1815-0659 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147391 |
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| Zitieren: | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms / M.C. Hay // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707123616481280 |
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| author | Hay, M.C. |
| author_facet | Hay, M.C. |
| citation_txt | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms / M.C. Hay // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms within the Lax matrices to be zero. We cover all possible Lax pairs of this type and find a new third order equation that can be reduced to special cases of the non-autonomous lattice KdV and lattice modified KdV equations among others.
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| first_indexed | 2025-12-07T17:03:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147391 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:03:39Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hay, M.C. 2019-02-14T17:00:38Z 2019-02-14T17:00:38Z 2011 A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms / M.C. Hay // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K15; 39A14; 70H06 https://nasplib.isofts.kiev.ua/handle/123456789/147391 We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms within the Lax matrices to be zero. We cover all possible Lax pairs of this type and find a new third order equation that can be reduced to special cases of the non-autonomous lattice KdV and lattice modified KdV equations among others. This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html.
 The author appreciatively acknowledges support from the Global COE Program “Education and Research Hub for Mathematics-for-Industry” from the Ministry of Education, Culture, Sports, Science and Technology, Japan. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms Article published earlier |
| spellingShingle | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms Hay, M.C. |
| title | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms |
| title_full | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms |
| title_fullStr | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms |
| title_full_unstemmed | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms |
| title_short | A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms |
| title_sort | completeness study on certain 2×2 lax pairs including zero terms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147391 |
| work_keys_str_mv | AT haymc acompletenessstudyoncertain22laxpairsincludingzeroterms AT haymc completenessstudyoncertain22laxpairsincludingzeroterms |