Perturbation theory based on the Riemann problem for the Landau-Lifshitz equation (Q916003)

The perturbed Landau-Lifshitz equation \[ \vec S_ t=[\vec S\times \vec S_{xx}]+[\vec S\times \hat J\vec S]+\epsilon \vec R(\vec S), \] describing the nonlinear dynamics of the magnetization field in a one- dimensional ferromagnetic model is analysed. Here \(\vec S\) is the unit magnetization vector, \(\hat J=diag(J_ 1,J_ 2,J_ 3)\), and \(\epsilon\) is a small perturbative parameter. Perturbation theory based on the Riemann problem on the torus is constructed to derive evolution equations describing the perturbation-induced dynamics of the scattering data arising in the inverse scattering transform. The perturbation theory is applied to analyse the influence of small perturbations on the dynamics of domain walls and magnetic solitons. In particular, the scattering of the domain wall by a local inhomogeneity under the external magnetic field and dissipation is studied. With the help of the approach developed the radiation-induced damping of the magnetic soliton and the inelastic scattering of the domain walls of opposite polarities are analysed, too.