BOUNDARY-VALUE PROBLEM FOR 2-DIMENSIONAL STATIONARY HEISENBERG MAGNET WITH NONTRIVIAL BACKGROUND .1.

The method of the inverse scattering transform is used to solve a boundary-value problem on the half-plane for the two-dimensional stationary Heisenberg magnet with nontrivial background corresponding to helicoidal magnetic structures. The boundary conditions are formulated in terms of scattering data, and this leads to the appearance of gaps in the continuous spectrum of the auxiliary linear problem. Trace identities are obtained. The asymptotic behavior of some of the simplest solutions of "soliton" type is discussed.