Perturbation of solitons in the classical continuum isotropic Heisenberg spin system

The dynamics of a one-dimensional classical continuum isotropic Heisenberg ferromagnetic spin system in the presence of a weak relativistic interaction, which causes damping of the spin motion, is considered. The corresponding evolution equation is identified with a damped nonlinear Schrödinger equation in terms of the energy and current densities of the unperturbed system. A direct perturbation method, along the lines of Kodama and Ablowitz, is developed for the envelope soliton solution of the nonlinear Schrödinger equation and the explicit perturbed solution obtained. This solution is found to be valid in a finite domain of the propagation space. To cover the entire region, a uniform solution is constructed using the matched asymptotic expansion technique. Finally, the spin vectors are constructed using the known procedures in differential geometry and the consequences of damping analysed briefly.