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The gauge equivalent structure of the Landau-Lifshitz equation and its applications. (English) Zbl 1071.82573
Summary: By introducing the conception of given curvature formulation for partial differential equations, we show that the Landau–Lifshitz equation (LLE) is gauge equivalent to a nonlinear Schrödinger-like equation, which answers a question proposed by Bordag and Yanovski. As a direct consequence, explicit first-order approximate 1-soliton solutions (with respect to the interaction anisotropy) to the LLE are constructed from those to the nonlinear Schrödinger-like equation.

MSC:
82D40 Statistical mechanical studies of magnetic materials
35Q55 NLS equations (nonlinear Schrödinger equations)
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