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On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations. (English) Zbl 1168.37019

The Adler-Bobenko-Suris (ABS) lattice equations are studied. Analysis of their transformation properties is given, and Miura transformations between the ABS equations and Volterra-type difference equations are presented.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37L20 Symmetries of infinite-dimensional dissipative dynamical systems
39A05 General theory of difference equations
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