完全各向同性Landau-Lifischitz方程孤子解的验证  

Demonstration of Soliton Solutions of the Isotropic Landau-Lifaschitz equation

作　　者：李存[1] 宋宣玉[1] 张新伟[1] 张东玲[1] 

机构地区：[1]信阳师范学院物理电子工程学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2010年第1期50-53,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：信阳师范学院青年教师科研基金项目(200954)

摘　　要：在建立Landau-Lifschitz方程的反散射变换方程的过程中,引入因子λ1来保证当λ趋于无穷大时沿复平面的上半圆弧的积分贡献为零.为了验证由此得到的解的正确性,将Landau-Lifschitz方程的约斯特解构建为具有与2×2矩阵相同性质的形式,并由Liouville定理引入另一对约斯特解作为前一对的右逆,由2×2矩阵的性质知所引入的约斯特解也可以作为其左逆.由此代入验证约斯特解完全满足Lax方程.This paper introduced a redundant factor λ-1 in constructing inverse scattering transform to ensure vanishing contribution of the integral along big semi-circle in upper half plane of complex λ as the radius tends to infinite.In order to verify the correctness of the solutions,this paper introduced a pair of Jost solutions with the same analytic properties of a 2×2 matrix,and then another pairs was introduced to be its right inverse confirmed by the Liouville theorem.Because they are both 2×2 matrices,the right inverse should be the left inverse too,furthemore,it is not difficult to show that these Jost solutions satisfy both Lax equations.As a result of compatibility condition,the soliton solutions definitely satisfy the L-L equation in the reflectionless.

关 键 词：Landau-Lifschitz方程 约斯特解 孤子解 LIOUVILLE定理 

分 类 号：O411.1[理学—理论物理]