On integrability of the Yang-Baxter σ-model

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.