Landau-Lifshitz方程派生的球面锥对称族及其演化

Spherical cone symmetric families generated by Landau-Lifshitz equation and their evolution

直至2008年,尚未见到讨论同时具有外磁场和各向异性场的多维Landau-Lifshitz方程的显式动态解的文献.当缺少外加磁场或各向异性场时,许多作者曾经尝试过Hirota的著名方法,Lie代数结构与Backlund变换,双线性变换等,但精确解仍然没有构造出来.本文首先给出了一种求解具有外磁场和各向异性场的Landau-Lifshitz方程的一种方法,并得到了Landau-Lifshitz方程的一族新型对称的解,我们称之为球面锥对称解.然后,我们将揭示这些解如何随时间变化而演化.最后,我们给出一系列显式动态球面锥对称解.

Until 2008,we had not seen a paper about the explicit dynamic solution of the multi-dimensional Landau-Lifshitz equation with the external magnetic field and anisotropy field.In the absence of an external magnetic field or anisotropy field,many experts have tried Hirota’s famous method,Lie algebra structure and Backlund transformations,bilinear transform,but the exact solution is still not constructed.This paper presents a method to solve the Landau-Lifshitz equations with the external magnetic field and anisotropy field,and a new family of symmetric solutions,which we call it as spherical cone symmetric solution.Then,we shall show how these solutions evolve as time.Finally,we give a series of explicit dynamic spherical cone symmetric solutions.