  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 parameterised in
terms of initial data and the resulting covariant phase spaces are
diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson
brackets of the parameters of the solutions and give the general static
solutions for the affine theory.
