Investigation of nonlinear one-dimensional systems by means of the Hamiltonian formalism

A method is proposed for investigating the solutions of the weakly perturbed sine–Gordon equation by means of action–angle variables. The Green's function of radiation on the background of many-soliton solutions is calculated in the first approximation in the amplitude. The dynamics of one- and two-soliton solutions is investigated. The Landau–Lifshitz equation (including the nonintegrable modifications) is reduced in a special case to the perturbed sine–Gordon equation. Some solutions are investigated.