Landau-Lifshitz equation: solitons, quasi-periodic solutions and infinite-dimensional Lie algebras
Landau-Lifshitz equation: solitons, quasi-periodic solutions and infinite-dimensional Lie algebras
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DOI：
10.1088/0305-4470/16/2/006
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发表时间：
1983-02
期刊：
影响因子：
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通讯作者：
E. Date;M. Jimbo;M. Kashiwara;T. Miwa
中科院分区：
文献类型：
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作者：
E. Date;M. Jimbo;M. Kashiwara;T. Miwa
用椭圆曲线上的自由费米子φ（P）表示了具有全各向异性的Landau-Lifshitz方程S_1 =S* S_x ~ x +S* S_s的族.一个由phi（P）的二次型张成的无限维李代数被证明作为无穷小的Backlund变换作用于解。在波函数的双线性恒等式的基础上，证明了一个N孤子公式，并构造了拟周期解。
The hierarchy of the Landau-Lifshitz equation S1=S*Sxx+S*JS with full anisotropy is formulated in terms of a free fermion phi (P) on an elliptic curve. An infinite-dimensional Lie algebra spanned by quadratic forms of phi (P) is shown to act on solutions as infinitesimal Backlund transformations. On the basis of a bilinear identity of wavefunctions, an N-soliton formula is proved and quasi-periodic solutions are constructed.