Yang?Baxter maps and multi-field integrable lattice equations

A variety of Yang-Baxter maps are obtained from integrable multi-field equations on quad-graphs. A systematic framework for investigating this connection relies on the symmetry groups of the equations. The method is applied to lattice equations introduced by Adler and Yamilov, which are related to the nonlinear superposition formulae for the Backlund transformations of the nonlinear Schrodinger system and specific ferromagnetic models.