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TMF, 1997, Volume 110, Number 1, Pages 98–113 (Mi tmf955)  

This article is cited in 20 scientific papers (total in 20 papers)

Boundary value problem for the KdV equation on a half-line

V. E. Adlera, I. T. Habibullina, A. B. Shabatb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: The $L$$A$ pair corresponding to the boundary value problem with the condition $u|_{x=0}=a$ for the KdV equation is presented. A broad class of exact solutions to this equation is constructed and the conservation laws are discussed.


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English version:
Theoretical and Mathematical Physics, 1997, 110:1, 78–90

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Received: 01.08.1996

Citation: V. E. Adler, I. T. Habibullin, A. B. Shabat, “Boundary value problem for the KdV equation on a half-line”, TMF, 110:1 (1997), 98–113; Theoret. and Math. Phys., 110:1 (1997), 78–90

Citation in format AMSBIB
\by V.~E.~Adler, I.~T.~Habibullin, A.~B.~Shabat
\paper Boundary value problem for the KdV equation on a half-line
\jour TMF
\yr 1997
\vol 110
\issue 1
\pages 98--113
\jour Theoret. and Math. Phys.
\yr 1997
\vol 110
\issue 1
\pages 78--90

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    This publication is cited in the following articles:
    1. Adler, V, “Boundary conditions for integrable equations”, Journal of Physics A-Mathematical and General, 30:10 (1997), 3505  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Gurel, B, “Boundary conditions for two-dimensional integrable chains”, Physics Letters A, 233:1–2 (1997), 68  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, Theoret. and Math. Phys., 114:1 (1998), 90–98  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. I. T. Habibullin, “KdV equation on a half-line with the zero boundary condition”, Theoret. and Math. Phys., 119:3 (1999), 712–718  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. T. Habibullin, “An Initial-Boundary Value Problem on the Half-Line for the MKdV Equation”, Funct. Anal. Appl., 34:1 (2000), 52–59  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. T. Habibullin, “Initial Boundary Value Problem for the KdV Equation on a Semiaxis with Homogeneous Boundary Conditions”, Theoret. and Math. Phys., 130:1 (2002), 25–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Fokas, AS, “Integrable Nonlinear evolution equations on the half-line”, Communications in Mathematical Physics, 230:1 (2002), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    8. A. B. Shabat, “Universal Models of Soliton Hierarchies”, Theoret. and Math. Phys., 136:2 (2003), 1066–1076  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Fokas, AS, “Linearizable initial boundary value problems for the sine-Gordon equation on the half-line”, Nonlinearity, 17:4 (2004), 1521  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. Fokas, AS, “The nonlinear Schrodinger equation on the half-line”, Nonlinearity, 18:4 (2005), 1771  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    11. V. L. Vereshchagin, “Integrable boundary-value problem for the Volterra chain on the half-axis”, Math. Notes, 80:5 (2006), 658–662  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Gurses, M, “Integrable boundary value problems for elliptic type Toda lattice in a disk”, Journal of Mathematical Physics, 48:10 (2007), 102702  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    13. Fokas A.S., “Lax pairs: a novel type of separability”, Inverse Problems, 25:12 (2009), 123007  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    14. V. L. Vereshchagin, “Explicit solutions of an integrable boundary value problem for the two-dimensional Toda lattice”, Theoret. and Math. Phys., 165:1 (2010), 1256–1261  mathnet  crossref  crossref  adsnasa  isi
    15. Vereschagin V.L., “Integrable boundary problems for 2D Toda lattice”, Phys Lett A, 374:46 (2010), 4653–4657  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    16. M. Yu. Ignatev, “O resheniyakh nekotorykh kraevykh zadach dlya obschego uravneniya KdF”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:1(2) (2013), 46–49  mathnet
    17. Ignatyev M.Yu., “On Solutions of the Integrable Boundary Value Problem for KdV Equation on the Semi-Axis”, Math. Phys. Anal. Geom., 16:1 (2013), 19–47  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    18. Ignatyev M.Yu., “On Solution of the Integrable Initial Boundary Value Problem for KdV Equation on the Semi-Axis”, Math. Phys. Anal. Geom., 16:4 (2013), 381–392  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. Ignatyev M.Yu., “On the Solutions of Some Boundary Value Problems For the General KdV Equation”, Math. Phys. Anal. Geom., 17:3-4 (2014), 493–509  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    20. Habibullin I.T., Khakimova A.R., “On a Method For Constructing the Lax pairs For Integrable Models Via a Quadratic Ansatz”, J. Phys. A-Math. Theor., 50:30 (2017), 305206  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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