On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations

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dc.creatorLevi, Decio
dc.creatorPetrera, Matteo
dc.creatorScimiterna, Christian
dc.creatorYamilov, Ravil
dc.date2008-02-13
dc.date2008-11-08
dc.date.accessioned2026-07-07T10:16:37Z
dc.date.available2026-07-07T10:16:37Z
dc.descriptionWe 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0802.1850
dc.identifierhttp://arxiv.org/abs/0802.1850
dc.identifierSIGMA 4 (2008), 077, 14 pages
dc.identifierdoi:10.3842/SIGMA.2008.077
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173570
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
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