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

A connection between the Yang-Baxter relation for maps and the multidimensional 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 multiparameter 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 multifield integrable equations.