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Initial Boundary-Value Problems for Soliton Equations

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Book cover Nonlinear Processes in Physics

Part of the book series: Springer Series in ((SSNONLINEAR))

Abstract

A method is presented for linearizing initial-boundary value problems for integrable nonlinear evolution equations with the spatial variable on an half-infinite line. This method yields the solution of a nonlinear equation in terms of the solution of two linear integral equations, whose analysis for large t, shows how the boundary conditions can generate solitons.

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References

  1. C.K. Chu and R.L. Chou, Advances in Applied Mechanics, 27 283–302 (1990).

    Article  MathSciNet  Google Scholar 

  2. D.J. Kaup and P. Wycoff, Stud. Appl. Math. 81 7–20 (1989).

    MathSciNet  MATH  Google Scholar 

  3. A.S. Fokas, Physics D 35, 167–185 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. M.J. Ablowitz and H. Segur, J. Math. Phys. 16 1054 (1975).

    Article  ADS  MATH  Google Scholar 

  5. E.K. Sklyanin, Funk. Analiz. (Func. Anal. Appl.) 21 (2), 86–7 (1987).

    MathSciNet  Google Scholar 

  6. R.F. Bikbaev and A.R. Its, Matem. Zametki (Math. Notes) 45 (3) 3–10 (1989).

    MathSciNet  Google Scholar 

  7. V.O. Tarasov, Inverse Problems 7 435–449 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. A.S. Fokas and M.J. Ablowitz, Stud. in Appl. Math. 80, 253–272 (1989).

    MathSciNet  MATH  Google Scholar 

  9. V.E. Zakharov and P.B. Shabat, Sov. Phys. JETP 34, 62 (1972).

    MathSciNet  ADS  Google Scholar 

  10. P.D. Lax, Comm. Pure Appl. Math., 21 467 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  11. X. Zhou, SIAM J. Math. Anal., 20 966–986 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Brenner, A.S. Fokas, A.R. Its, and L.Y. Sung, Analytical, Asymptotic, and Numerical Study of the NLS Equation on the Half-Infinite Line, (in preparation).

    Google Scholar 

  13. P. Deift and X. Zhou, to appear in Annals of Math. (1991).

    Google Scholar 

  14. I.M. Gel’fand and B.M. Levitan, Amer. Math. Soc. Transl. Ser. 2, 1 253 (1955).

    MathSciNet  MATH  Google Scholar 

  15. A.S. Fokas and P.M. Santini, Phys. Rev. Lett. 63 1329 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  16. A.S. Fokas and P.M. Santini, Physica D 44 99 (1990).

    Article  MathSciNet  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science and Institute of Nonlinear Studies, Clarkson University, Potsdam, NY, 13699-5815, USA

    A. S. Fokas

Authors
  1. A. S. Fokas
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Editor information

Editors and Affiliations

  1. Clarkson University, 13699-5815, Potsdam, NY, USA

    A. S. Fokas  & D. J. Kaup  & 

  2. University of Arizona, 85721, Tucson, AZ, USA

    A. C. Newell  & V. E. Zakharov  & 

  3. Landau Institute for Theoretical Physics, ul. Kosygina 2, 117334, Moscow, Russia

    V. E. Zakharov

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© 1993 Springer-Verlag Berlin Heidelberg

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Fokas, A.S. (1993). Initial Boundary-Value Problems for Soliton Equations. In: Fokas, A.S., Kaup, D.J., Newell, A.C., Zakharov, V.E. (eds) Nonlinear Processes in Physics. Springer Series in Nonlinear Dynamics . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77769-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-77769-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77771-4

  • Online ISBN: 978-3-642-77769-1

  • eBook Packages: Springer Book Archive

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