On The 1+2 Dimensional Landau-Lifshitz Equation

Details On The 1+2 Dimensional Landau-Lifshitz Equation On The 1+2 Dimensional Landau-Lifshitz Equation

2005-04-14

arxiv.org/abs/math/0504288v1

Mathematics

Differential Geometry

26 pages without figures

Scientific paper

By using the geometric concept of PDEs with prescribed curvature representations, we show that the 1+2 dimensional Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schr\"odinger-type system. From the nonlinear Schr\"odinger-type system, we construct blowing up $H^3({\bf R}^2)$-solutions to the 1+2 dimensional Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.

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