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Yang-Baxter maps and symmetries of integrable equations on quad-graphs
2006
Journal of Mathematical Physics
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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
doi:10.1063/1.2227641
fatcat:cp2bf2hfsvfr7gcstilukq7qca