On The 1+2 Dimensional Landau-Lifshitz Equation
Abstract
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 H3( R2)-solutions to the 1+2 dimensional Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.
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