On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
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| Creator |
Levi, D.
Petrera, M. Scimiterna, C. Yamilov, R. |
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| 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.
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| Date |
2019-02-19T12:54:07Z
2019-02-19T12:54:07Z 2008 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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