Stationary Structures in Two-Dimensional Continuous Heisenberg Ferromagnetic Spin System

Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2 + 1)-dimensional Landau–Lifshitz model. It is established that in the case of ~ S(~r, t) = ~ S(~r − ~vt) the Landau–Lifshitz equation is closely related to the Ablowitz–Ladik hierarchy. This relation is used to obtain soliton structures, which are shown to be caused by joint action of nonlinearity and spatial dispersion, contrary to the well-known one-dimensional solitons which exist due to competition of nonlinearity and temporal dispersion. We also present elliptical quasiperiodic stationary solutions of the stationary (2 + 1)dimensional Landau–Lifshitz equation.