Soliton damping and energy loss in the classical continuum Heisenberg spin chain

We consider the effect of damping on the evolution of a classical continuum one-dimensional isotropic Heisenberg ferromagnetic spin chain due to relativistic interaction. The corresponding Landau-Lifshitz equation is shown to be identifiable with a damped nonlinear Schrödinger equation. By obtaining an explicit decaying solitary wave solution for the energy density and magnetization density, we demonstrate the damping of the soliton solution with an associated loss of the total energy.