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TMF, 1999, Volume 119, Number 3, Pages 397–404 (Mi tmf747)  

This article is cited in 8 scientific papers (total in 8 papers)

KdV equation on a half-line with the zero boundary condition

I. T. Habibullin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We solve the mixed problem for the KdV equation with the boundary condition $u|_{x=0}=0$, $u_{xx}|_{x=0}=0$ using the inverse scattering method. The time evolution of the scattering matrix is efficiently defined from the consistency condition for the spectra of two differential operators giving the $L$$A$ pair.

DOI: https://doi.org/10.4213/tmf747

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English version:
Theoretical and Mathematical Physics, 1999, 119:3, 712–718

Bibliographic databases:

Received: 29.10.1998

Citation: I. T. Habibullin, “KdV equation on a half-line with the zero boundary condition”, TMF, 119:3 (1999), 397–404; Theoret. and Math. Phys., 119:3 (1999), 712–718

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 1999
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\pages 712--718
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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, “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
    2. 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
    3. de Monvel, AB, “Generation of asymptotic solitons of the nonlinear Schrodinger equation by boundary data”, Journal of Mathematical Physics, 44:8 (2003), 3185  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. 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
    5. de Monvel, AB, “Characteristic properties of the scattering data for the mKdV equation on the half-line”, Communications in Mathematical Physics, 253:1 (2005), 51  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Khanmamedov A.K., “On the integration of an initial-boundary value problem for the Volterra lattice”, Differential Equations, 41:8 (2005), 1192–1195  mathnet  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Pham Loi Vu, “An Initial-Boundary Value Problem for the Korteweg-de Vries Equation with Dominant Surface Tension”, Acta Appl. Math., 129:1 (2014), 41–59  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Pham Loi Vu, “The Description of Reflection Coefficients of the Scattering Problems For Finding Solutions of the Korteweg-de Vries Equations”, J. Nonlinear Math. Phys., 25:3 (2018), 399–432  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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