Deformed integrableσ-models, classicalR-matrices and classical exchange algebra on Drinfel’d doubles

We describe a unifying framework for the systematic construction of integrable deformations of integrable σ -models within the Hamiltonian formalism. It applies equally to both the 'Yang–Baxter' type as well as 'gauged WZW' type deformations which were considered recently in the literature. As a byproduct, these two families of integrable deformations are shown to be Poisson–Lie T -dual of one another.