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TMF, 1992, Volume 91, Number 3, Pages 363–376 (Mi tmf5584)  

This article is cited in 7 scientific papers (total in 7 papers)

Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method

I. T. Habibullin

Bashkir State University

Abstract: Examples of boundary conditions compatible with the integrability property of the Ishimori equation are found by adjoining a point symmetry of reflection type to Bficklund and Miura transformations. Soliton solutions of the corresponding boundary-value problems on the half- and quarter-plane are constructed. The interaction of the boundary with the solitons is investigated.

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English version:
Theoretical and Mathematical Physics, 1992, 91:3, 581–590

Bibliographic databases:

Received: 10.01.1992

Citation: I. T. Habibullin, “Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method”, TMF, 91:3 (1992), 363–376; Theoret. and Math. Phys., 91:3 (1992), 581–590

Citation in format AMSBIB
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\by I.~T.~Habibullin
\paper Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method
\jour TMF
\yr 1992
\vol 91
\issue 3
\pages 363--376
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1187016}
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\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 91
\issue 3
\pages 581--590
\crossref{https://doi.org/10.1007/BF01017333}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. T. Habibullin, “Boundary conditions for nonlinear equations compatible with integrability”, Theoret. and Math. Phys., 96:1 (1993), 845–853  mathnet  crossref  mathscinet  zmath  isi
    2. A. B. Borisov, “Asymptotic behavior of singular solitons and the inverse scattering method for solving boundary value problems”, Theoret. and Math. Phys., 124:2 (2000), 1094–1104  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    4. I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funct. Anal. Appl., 38:2 (2004), 138–148  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Vereschagin V.L., “Integrable boundary problems for 2D Toda lattice”, Phys Lett A, 374:46 (2010), 4653–4657  crossref  isi
    6. V. L. Vereshchagin, “Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics”, Theoret. and Math. Phys., 171:3 (2012), 792–799  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    7. V. L. Vereshchagin, “Explicit Solutions of Boundary-Value Problems for $(2+1)$-Dimensional Integrable Systems”, Math. Notes, 93:3 (2013), 360–372  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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