Landau-Lifshitz equation: solitons, quasi-periodic solutions and infinite-dimensional Lie algebras
- 1 February 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (2) , 221-236
- https://doi.org/10.1088/0305-4470/16/2/006
Abstract
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.Keywords
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