Abstract
The Cauchy problem for the Landau-Lifshitz equation of one-dimensional ferromagnets with biaxial anisotropy can be reduced to the inverse scattering problem for the L-M pair and then to the 2×2 matrix Riemann problem for a torus. The solvability of this problem in the class of holomorphic matrices is not investigated till now. Nonsolvability of this problem could mean that whether some scattering data correspond to no initial wave configuration or the wave collapses at some moment of time. This situation is typical, apparently, for reflective finite-zone potentials. In this paper we consider the solitonless case for fast-decreasing potentials. We show that the matrix Riemann problem and, hence, the inverse scattering problem are solvable in this case.
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