On integrability of the Yang–Baxter σ-model

We prove that the recently introduced Yang–Baxter σ-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.