Abstract
We present the Hamiltonian formulation of the recently constructed integrable theories of [49]. These theories turn out to be canonically equivalent to the sum of an asymmetrically gauged CFT and of the most general λ-deformed model of [21]. Using the Hamiltonian formalism, we prove that the full set of conserved charges of the models of [49] are in involution, ensuring their Hamiltonian integrability. Finally, we show that the equations of motion of these theories can be put in the form of zero curvature Lax connections.
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