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TMF, 1992, Volume 90, Number 2, Pages 259–272 (Mi tmf5534)  

This article is cited in 6 scientific papers (total in 6 papers)

Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I

E. Sh. Gutshabash, V. D. Lipovskii

Scientific-Research Institute of Leningrad State University

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1992, 90:2, 175–184

Bibliographic databases:

Received: 29.04.1991

Citation: E. Sh. Gutshabash, V. D. Lipovskii, “Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I”, TMF, 90:2 (1992), 259–272; Theoret. and Math. Phys., 90:2 (1992), 175–184

Citation in format AMSBIB
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\by E.~Sh.~Gutshabash, V.~D.~Lipovskii
\paper Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background.~I
\jour TMF
\yr 1992
\vol 90
\issue 2
\pages 259--272
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1182298}
\zmath{https://zbmath.org/?q=an:0798.35142}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 90
\issue 2
\pages 175--184
\crossref{https://doi.org/10.1007/BF01028442}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JT83800010}


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    This publication is cited in the following articles:
    1. G. G. Varzugin, E. Sh. Gutshabash, V. D. Lipovskii, “Boundary-value problem for the two-dimensional stationary Heisenberg magnet with non-trivial background. II”, Theoret. and Math. Phys., 104:3 (1995), 1166–1177  mathnet  crossref  mathscinet  zmath  isi
    2. E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of $(2+0)$-dimensional integrable equations”, Theoret. and Math. Phys., 115:3 (1998), 619–638  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. E. Sh. Gutshabash, “Generalized Darboux transform in the Ishimori magnet model on the background of spiral structures”, JETP Letters, 78:11 (2003), 740–744  mathnet  crossref
    4. E. Sh. Gutshabash, “On canonical variables for integrable models of magnets”, J. Math. Sci. (N. Y.), 151:2 (2008), 2865–2879  mathnet  crossref  mathscinet
    5. E. Sh. Gutshabash, P. P. Kulish, “Discrete symmetries, Darboux transformation, and exact solutions of the Wess–Zumino–Novikov–Witten model”, J. Math. Sci. (N. Y.), 158:6 (2009), 845–852  mathnet  crossref  zmath
    6. JETP Letters, 89:1 (2009), 1–5  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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