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 TMF, 1991, Volume 86, Number 1, Pages 43–52 (Mi tmf5419)

Integrable initial-boundary-value problems

I. T. Habibullin

Abstract: Initial-boundary-value problems on a half-axis for integrable equations are considered. Solutions of an initial-boundary-value problem for the nonlinear Schrödinger equation and the sine-Gordon equation for definite types of boundary conditions are described in terms of scattering data.

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English version:
Theoretical and Mathematical Physics, 1991, 86:1, 28–36

Bibliographic databases:

Citation: I. T. Habibullin, “Integrable initial-boundary-value problems”, TMF, 86:1 (1991), 43–52; Theoret. and Math. Phys., 86:1 (1991), 28–36

Citation in format AMSBIB
\Bibitem{Hab91} \by I.~T.~Habibullin \paper Integrable initial-boundary-value problems \jour TMF \yr 1991 \vol 86 \issue 1 \pages 43--52 \mathnet{http://mi.mathnet.ru/tmf5419} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1106826} \zmath{https://zbmath.org/?q=an:0728.35114} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 1 \pages 28--36 \crossref{https://doi.org/10.1007/BF01018494} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GC79000004} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. T. Habibullin, “Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method”, Theoret. and Math. Phys., 91:3 (1992), 581–590
2. I. T. Habibullin, “Boundary conditions for nonlinear equations compatible with integrability”, Theoret. and Math. Phys., 96:1 (1993), 845–853
3. V. V. Gudkov, “Explicit form of the wave solutions of evolution equations”, Comput. Math. Math. Phys., 36:3 (1996), 335–340
4. V. E. Adler, I. T. Habibullin, A. B. Shabat, “Boundary value problem for the KdV equation on a half-line”, Theoret. and Math. Phys., 110:1 (1997), 78–90
5. I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, Theoret. and Math. Phys., 114:1 (1998), 90–98
6. I. T. Habibullin, “KdV equation on a half-line with the zero boundary condition”, Theoret. and Math. Phys., 119:3 (1999), 712–718
7. I. T. Habibullin, “An Initial-Boundary Value Problem on the Half-Line for the MKdV Equation”, Funct. Anal. Appl., 34:1 (2000), 52–59
8. Gurses, M, “Integrable boundary value problems for elliptic type Toda lattice in a disk”, Journal of Mathematical Physics, 48:10 (2007), 102702
9. Kundu, A, “Changing Solitons in Classical & Quantum Integrable Defect and Variable Mass sine-Gordon Model”, Journal of Nonlinear Mathematical Physics, 15 (2008), 237
10. Shamsutdinov, MA, “Dynamics of magnetic kinks in exchange-coupled ferromagnetic layers”, Physics of Metals and Metallography, 108:4 (2009), 327
11. Biondini G. Bui A., “On the Nonlinear Schrodinger Equation on the Half Line with Homogeneous Robin Boundary Conditions”, Stud. Appl. Math., 129:3 (2012), 249–271
12. Aguirre A.R., Gomes J.F., Ymai L.H., Zimerman A.H., “N=1 Super Sinh-Gordon Model in the Half Line: Breather Solutions”, J. High Energy Phys., 2013, no. 4, 136
13. Lima F.C. Simas F.C. Nobrega K.Z. Gomes A.R., “Boundary Scattering in the Phi(6) Model”, J. High Energy Phys., 2019, no. 10, 147
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