On The 1+2 Dimensional Landau-Lifshitz Equation

2005/04/14 by Qing Ding, Ding, Qing
Mathematics · Physics and Astronomy · #35E55 #58E20 #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics #math-ph #math.DG #math.MP #msc:35E55 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0504288

26 pages without figures

arxiv created 2005/04/14 · openalex publication_date 2005/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger-type system. From the nonlinear Schrödinger-type system, we construct blowing up H³(\bf R²)-solutions to the 1+2 dimensional Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.

Citations

• Existence of solitary waves in higher dimensions

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