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

Vassilios G. Papageorgiou, Anastasios G. Tongas, Alexander P. Veselov
2006 Journal of Mathematical Physics  
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
more » ... ived in this way from multi-field integrable equations.
doi:10.1063/1.2227641 fatcat:cp2bf2hfsvfr7gcstilukq7qca