DMCA
On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations (2008)
| Venue: | SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS |
| Citations: | 15 - 8 self |
BibTeX
@MISC{Levi08onmiura,
author = {Decio Levi and Matteo Petrera and Christian Scimiterna and Ravil Yamilov},
title = {On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations},
year = {2008}
}
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Abstract
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.
Keyphrases
miura transformation adler bobenko suris equation volterra-type equation associated cklund transformation ydkn equation ab equation ab equation correspond discrete krichever novikov equation discrete schr dinger spectral problem scalar spectral problem integrable lattice equation volterra-type equation particular case present paper adler bobenko suris new generalized symmetry
