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On integrability of the Yang-Baxter $$\sigma$$-model. (English) Zbl 1215.81099
Summary: We prove that the recently introduced Yang-Baxter $$\sigma$$-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang-Baxter context.

##### MSC:
 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 81R12 Groups and algebras in quantum theory and relations with integrable systems
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