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New Manifestations of Solitons

  • A. S. Fokas
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 25)

Abstract

In spite of the fact that the concept of the soliton is twenty-five years old, new manifestations of solitons, both in physics and mathematics, are being discovered. We summarize here the occurrence of solitons for three interesting situations: For the nonlinear Schrödinger equation on the half-line, for the Davey-Stewartson equation with non-zero boundary conditions, and for a special type of cellular automaton.

Keywords

Cellular Automaton Soliton Solution Schrodinger Equation Linear Limit Nonlinear Schrodinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A.S. Fokas, An Initial-Boundary Value Problem for the Nonlinear Schrödinger Equation, Physica D 35 (1989), pp. 167–185.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    A.S. Fokas and P.M. Santini, Coherent Structures in Multidimensions, Phys. Rev. Lett (1988).Google Scholar
  3. [3]
    A.S. Fokas, Phys. Rev. Lett., 51 (1983), pp. 3–6.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    M. Boiti, J. Leon, L. Martina, and F. Pempinelli, Scattering of Localized Solitons in the Plane, Physics Lett. A, 132, (1988), pp. 432–439.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    F. Calogero and A. Degasperis, Spectral Transform and Solitons I, North Holland (1982).Google Scholar
  6. [6]
    A.S. Fokas, E. Papadopoulou and Y. Saridakis, Particles in Soliton Cellular Automata, Clarkson University (1988).Google Scholar
  7. [7]
    A.S. Fokas, E. Papadopoulou, Y. Saridakis and M.J. Ablowitz, Interactions of Simple Particles in Soliton Cellular Automata, Clarkson University (1988).Google Scholar
  8. [8]
    A.S. Fokas, E. Papadopoulou and Y. Saridakis, Soliton Cellular Automata, Clarkson University (1988).Google Scholar
  9. [9]
    J.K. Park, K. Steiglitz and W.P. Thurston, Physica D, 19 (1986), pp. 423–432.MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    K. Steiglitz, I. Kamal and A. Watson, IEEE Trans. on Computers, 37 (1988), pp. 138–145.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • A. S. Fokas
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA

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