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On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
Інший ID:
2000 Mathematics Subject Classification: 37K10; 37L20; 39A05
Посилання:
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.
Підтримка:
DL, MP and CS have been partially supported by PRIN Project Metodi geometrici nella teoria delle onde non lineari ed applicazioni-2006 of the Italian Minister for Education and Scientific Research. RY has been partially supported by the Russian Foundation for Basic Research (Grant numbers 07-01-00081-a and 06-01-92051-KE-a) and he thanks the University of Roma Tre for hospitality. This work has been done in the framework of the Project Classification of integrable discrete and continuous models financed by a joint grant from EINSTEIN consortium and RFBR.
Дата:
2008
Переглядів:
551
Завантажень:
255
Анотація:
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.
