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Exact solutions of a nonlinear sigma-model in a curved space and the theory of magnetically ordered media with variable saturation magnetization. (English. Russian original) Zbl 0931.35137
J. Math. Sci., New York 77, No. 2, 3063-3068 (1995); translation from Zap. Nauchn. Semin. POMI 199, 71-80 (1992).
Summary: Stationary solitons are found to occur in two-dimensional media with a variable saturation magnetization whose square is a harmonic function of the coordinates. It is shown in this case that the Landau-Lifshitz equation can be reduced to the integrable \(O(3)\) sigma-model in curved space. Some properties of the solutions obtained are discussed.
MSC:
35Q40 PDEs in connection with quantum mechanics
81T20 Quantum field theory on curved space or space-time backgrounds
82D40 Statistical mechanics of magnetic materials
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