Yang-Baxter maps and symmetries of integrable equations on quad-graphs

2006/05/08 by Vassilios G. Papageorgiou, Anastasios G. Tongas, Alexander P. Veselov · 3 citations
Mathematics · Physics and Astronomy · #math.QA #nlin.SI

paper · pdf · doi:10.1063/1.2227641

20 pages, 5 figures

arxiv created 2006/05/08 · arxiv updated 2015/06/26

Abstract

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.

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