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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 \vec S (\vec r, t)= \vec S (\vec r - \vec v t) 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.