Portal de Periódicos da CAPES

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

2006; American Institute of Physics; Volume: 47; Issue: 8 Linguagem: Inglês

10.1063/1.2227641

1527-2427

V. Papageorgiou, Anastasios Tongas, А. П. Веселов,

Advanced Topics in Algebra

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.