Local and nonlocal solitons in a coupled real system of Landau–Lifshitz equations

Abstract

We consider the gauge equivalence of all NLS-type reductions with a coupled system of Landau–Lifshitz equations. In the local case it is shown to reduce to the continuum limit of the classical isotropic Heisenberg ferromagnet equation. All nonlocal reductions, however, are shown to be equivalent to a two-sublattice antiferromagnetic system. Nonlocal solitons are shown to represent excitations from nonzero ground state magnetization and antiferromagnetic vectors, indicative of a ferrimagnetic system. An alternate geometric interpretation is given by means of a coupled Hasimoto transformation, establishing the connection between the nonlocal reductions of the AKNS system and the motion of a curve in ℂ3. Through Darboux transformations, the one-soliton solutions of the coupled LL equations are obtained.