4 research outputs found
Yang-Baxter maps and symmetries of integrable equations on quad-graphs
A connection between the Yang-Baxter relation for maps and the
multi-dimensional consistency property of integrable equations on quad-graphs
is investigated. The approach is based on the symmetry analysis of the
corresponding equations. It is shown that the Yang-Baxter variables can be
chosen as invariants of the multi-parameter symmetry groups of the equations.
We use the classification results by Adler, Bobenko and Suris to demonstrate
this method. Some new examples of Yang-Baxter maps are derived in this way from
multi-field integrable equations.Comment: 20 pages, 5 figure
Yang-Baxter maps and multi-field integrable lattice equations
A variety of Yang-Baxter maps are obtained from integrable multi-field
equations on quad-graphs. A systematic framework for investigating this
connection relies on the symmetry groups of the equations. The method is
applied to lattice equations introduced by Adler and Yamilov and which are
related to the nonlinear superposition formulae for the B\"acklund
transformations of the nonlinear Schr\"odinger system and specific
ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio