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Explicit solutions of the chain equations describing discrete transformations of the Landau-Lifshitz equation are found in the most economical way. This chain can be considered as a generalization of the Toda chain (the case of a rational spectral parame- ter) to the case of an elliptic curve. We show that the process of deriving multi-soliton solutions of the Landau-Lifshitz equation in an explicit form with help of these results becomes relatively straightforward.

Discrete Symmetry and Its Use to Find Multi-Soliton Solutions of the Equations of Anisotropic Heisenberg Ferromagnets