Levi, Decio; Petrera, Matteo; Scimiterna, Christian; Yamilov, Ravil On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations. (English) Zbl 1168.37019 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 077, 14 p. (2008). 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. Reviewer: Vjacheslav Yurko (Saratov) Cited in 8 Documents 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 Keywords:Miura transformations; ABS lattice equations PDFBibTeX XMLCite \textit{D. Levi} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 077, 14 p. (2008; Zbl 1168.37019) Full Text: DOI arXiv EuDML