Interacting domain walls in an easy-plane ferromagnet

Abstract

The Landau-Lifshitz equation for an anisotropic (easy-plane) ferromagnet is formulated as a Riemann-Hilbert problem on a Riemann surface of the spectral parameter. Exact multiple domain wall solutions can be obtained in a systematic and exhaustive manner by considering all possible pole arrangements on the Riemann surface. Explicit calculations for up to four poles have been carried out, yielding all possible double wall solutions, including states of colliding walls, breather modes of bound walls, and a set of solutions corresponding to marginally bound walls.