Geodesic
Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 259-272

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The method of the inverse scattering transform is used to solve a boundary-value problem on the half-plane for the twodimensional 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. 
@article{TMF_1992_90_2_a9,
     author = {E. Sh. Gutshabash and V. D. Lipovskii},
     title = {Boundary-value problem for two-dimensional stationary {Heisenberg} magnet with nontrivial {background.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {259--272},
     publisher = {mathdoc},
     volume = {90},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/}
}
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E. Sh. Gutshabash; V. D. Lipovskii. Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 259-272. http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a9/