铁磁链Landau-Lifshitz方程的显式差分法

正如在研究流体动力学时，Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程起着十分重要的作用一样，在对于非平衡态磁学的研究中，描述连续铁磁体自旋场发展过程的 Ｌａｎｄａｎ－Ｌｉｆｓｈｉｔｚ方程［１］起着十分重要的作用［２］．一九九三年，美国和印度签署了一个大约 ２８０万美元的合作研究计划，在三年的时间里，对Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ铁磁链方程进行研究．在无阻尼的情况下，它为一完全可积的孤立子系统［３，４，５］。很多物理学家研究了它的孤立子解的存在性、逆散射方法以及相互碰撞［３，４，５］．关于解的存在性， Ａｌｏｎ…

AN EXPLICIT FINITE DIFFERENCE SCHEME FOR THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN

In this paper, the Landau-Lifshitz equation with periodic initial boundary valued problem which is govnered by ()/(t)=-1 ( )+2( ) is discreted by using the Euler-forword finite difference method. The proposed scheme is explicit so that the parallel algorithm can be used to simulate numerically on computer. Moreove, the convergence and stability of the proposed scheme are proved by the finite extensive method of the nonlinear function. Finally, the numerical experiments are provided to check the theoritical results.