On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund tr...
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| Дата: | 2008 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149004 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations / D. Levi, M. Petrera, C. Scimiterna, R. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1490042019-02-21T01:23:16Z On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations Levi, D. Petrera, M. Scimiterna, C. Yamilov, R. We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund transformations for some particular cases of the discrete Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis. All of them generate Bäcklund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability. 2008 Article On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations / D. Levi, M. Petrera, C. Scimiterna, R. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 31 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 37L20; 39A05 http://dspace.nbuv.gov.ua/handle/123456789/149004 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund transformations for some particular cases of the discrete Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis. All of them generate Bäcklund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability. |
| format |
Article |
| author |
Levi, D. Petrera, M. Scimiterna, C. Yamilov, R. |
| spellingShingle |
Levi, D. Petrera, M. Scimiterna, C. Yamilov, R. On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Levi, D. Petrera, M. Scimiterna, C. Yamilov, R. |
| author_sort |
Levi, D. |
| title |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations |
| title_short |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations |
| title_full |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations |
| title_fullStr |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations |
| title_full_unstemmed |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations |
| title_sort |
on miura transformations and volterra-type equations associated with the adler-bobenko-suris equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149004 |
| citation_txt |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations / D. Levi, M. Petrera, C. Scimiterna, R. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 31 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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