Physics – Mathematical Physics
Scientific paper
2008-02-13
SIGMA 4 (2008), 077, 14 pages
Physics
Mathematical Physics
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Scientific paper
10.3842/SIGMA.2008.077
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 Schr\"odinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to B\"acklund 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 B\"acklund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability.
Levi Decio
Petrera Matteo
Scimiterna Christian
Yamilov Ravil
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