Group Invariant Solutions And Stability Of Multidimensional Landau - Lifshitz Equations

Landau-Lifshitz equation describes magnetization movement patterns of the magnetization media, so it plays an important role in ferromagnetic theory. In this paper, based on classical Lie Group method, we get the infinitesimal generator and group invariant solutions of Landau-Lifshitz equation. Then through the known solutions, we can obtain the multidimentional expilcit solutions. Taking advantage of some special solutions, we study the stability and uniqueness of initial-boundary problem on Landau-Lifshitz equation.In addition, we establish the finite difference scheme of the multidimensional Landau-Lifshitz equation for the initial-boundary value problems and analyse the truncation error of the difference scheme. Finally, we simulate the difference and compare with the exact solutions by Matlab software and verify the theoretical results for the stability of solutions.