The stability of localized solutions of Landau‐Lifshitz equations

We study the Landau‐Lifshitz equation of ferromagnetism on ?², with an easy‐axis anisotropy. We establish the existence of topologically nontrivial, periodic solutions, and show they are stable against equivariant perturbations. Along the way, we establish the global well‐posedness of the Cauchy problem for a class of data with no size restriction. © 2002 Wiley Periodicals, Inc.