Abstract
We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parametrized in terms of initial data and the resulting covariant phase spaces are diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson brackets to the parameters of the solutions and give the general static solutions for the affine theory.
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