On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E, in press

Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets

A parametrically forced sine-Gordon equation with a fast periodic {\em mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a class of solitary-wave solutions of the equation. This result is applied to quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly oscillating magnetic field. In this case the $\pi$-kink solution we have introduced corresponds to the uniform ``true'' domain wall motion, since the magnetization directions on opposite sides of the wall are anti-parallel. In contrast to previous work, no additional anisotropy is required to obtain a true domain wall. Numerical simulations showed good qualitative agreement with the theory.Comment: 3 pages, 1 figure, revte