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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Published in | Symmetry, integrability and geometry, methods and applications Vol. 4; p. 077 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Kiev
National Academy of Sciences of Ukraine
01.01.2008
National Academy of Science of Ukraine |
Subjects | |
Online Access | Get full text |
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Summary: | 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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ISSN: | 1815-0659 1815-0659 |
DOI: | 10.3842/SIGMA.2008.077 |