Theoretical and Mathematical Physics

, Volume 110, Issue 1, pp 78–90 | Cite as

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

  • V. E. Adler
  • L. T. Habibullin
  • A. B. Shabat


The L-A pair corresponding to the boundary value problem with the conditionu| 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.


Soliton Spectral Curve Integrable Boundary Condition Symmetry Approach Inverse Scattering Transform 
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  1. 1.
    M. J. Ablowitz and H. Segur,J. Math. Phys.,16, 1054 (1975).zbMATHCrossRefADSGoogle Scholar
  2. 2.
    A. S. Fokas,Physica D,35, 167 (1989).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    V. O. Tarasov,Inverse Problems,7, 435 (1991).zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    I. T. Habibullin,Theor. Math. Phys.,86, 28 (1991).CrossRefGoogle Scholar
  5. 5.
    E. Corrigan, P. E. Dorey, R. H. Rietdijk, and R. Sasaki, “Affine Toda field theory on a half-line,” hep-th/9404108 (1994).Google Scholar
  6. 6.
    An Ton Bui,J. Differ. Eq.,25, No. 3, 288 (1977).zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. 7.
    A. V. Faminskii,Tr. Mosk. Mat. Obshch.,51, 54 (1988).Google Scholar
  8. 8.
    M. D. Ramazanov,Mat. Sb.,64, No. 2, 234 (1964).MathSciNetGoogle Scholar
  9. 9.
    V. Adler, B. Gürel, M. Gürses, and I. Habibullin, “Boundary conditions for integrable equations,” (1996), to appear inJ. Phys. A.Google Scholar
  10. 10.
    I. T. Habibullin,Phys. Lett. A,178, 369 (1993).CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    I. T. Habibullin,Mat. Zam.,49, No. 4, 130 (1991).Google Scholar
  12. 12.
    B. Gürel, M. Gürses, and I. Habibullin,J. Math. Phys.,36, 6809 (1995).zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    H. E. Moses,J. Math. Phys.,17, 73 (1976).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    I. Kay and H. E. Moses,J. Appl. Phys.,27, 1503 (1956).zbMATHCrossRefADSGoogle Scholar
  15. 15.
    A. B. Shabat,Dinamika Sploshnoi Sredy,5, 130 (1970).Google Scholar
  16. 16.
    R. F. Bikbaev and V. O. Tarasov,Algebra Anal.,3, No. 4, 78 (1991).zbMATHMathSciNetGoogle Scholar
  17. 17.
    E. K. Sklyanin,Funkts. Anal. Prilozhen.,21, 86 (1987).MathSciNetGoogle Scholar
  18. 18.
    S. Ghoshal and A. B. Zamolodchikov, “Boundary state and boundaryS-matrix in two-dimensional integrable field theory,” Preprint RU-93-20; hep-th/9306002 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. E. Adler
    • 1
  • L. T. Habibullin
    • 1
  • A. B. Shabat
    • 2
  1. 1.Mathematical InstituteUfa Scientific Center for the Russian Academy of SciencesUSSR
  2. 2.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesUSSR

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