Deformed integrable $σ$-models, classical $R$-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.

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