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Approximations for the Inverse Scattering Transform

  • D. J. Kaup
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

What I would like to present here is a discussion of some of the various techniques and approximations which have been found to be useful in the IST (inverse scattering transform) [1]. Although the IST is an exact method, its complexity does require that one be able to make use of some approximations. And while I shall be discussing approximations, let me note that I also shall be emphasizing the methods and not the mathematical details.

Keywords

Pulse Shape Soliton Solution Pump Pulse Incident Pump Power Langmuir Wave 
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.
    M.J. Ablowitz, D.J.Kaup, A.C. Newell. and H. Segur, Stud. Appl. Math. 53, 249 (1974).Google Scholar
  2. 2.
    Yugi Kodama, ‘Nearly Integrable Systems’, Preprint-Nagoya Univ.# DPND-11–83, (1983).Google Scholar
  3. 3.
    A.S. Fokas and M.J. Ablowitz, Stud. Appl. Math. 68, 1 (1983).Google Scholar
  4. 4.
    M.J. Ablowitz, D. Bar Yaacov, and A.S. Fokas, Stud. Appl. Math. 69, 135 (1983).Google Scholar
  5. 5.
    A.R. Osborne and T.L. Burch, Science 208, 451 (1980).CrossRefGoogle Scholar
  6. 6.
    R.T. Joseph, J. Phys. A 10, L255 (1977).CrossRefGoogle Scholar
  7. 7.
    T. Kubota, D.R.S. Bo, and L.D. Dobbs, J. Hydronaut. 12, 157 (1978).CrossRefGoogle Scholar
  8. 8.
    H.H. Chen and Y.C. Lee, Phys. Rev. Letters 43, 264 (1979).CrossRefGoogle Scholar
  9. 9.
    Y. Kodama, J. Satsuma, and M.J. Ablowitz, J. M.th. Phys. 23, 564 (1980).Google Scholar
  10. 10.
    A.B. Osborne, Poster session at Solitons ‘82, Scott Russell Centenary Conference, Edinburgh, Scotland (23 Aug. 1982 ).Google Scholar
  11. 11.
    P.D. Lax, Comm. Pure Appl. Math. 21, 467 (1968).Google Scholar
  12. 12.
    D.J. Kaup, Siam J. Appl. Math. 31, 121 (1976).Google Scholar
  13. 13.
    V.E. Zakharov and A.B Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Soviet Phys. JETP 34, 62 (1972)].Google Scholar
  14. 14.
    J.P. Keener and D.W. McLaughlin, Phys. Rev. A 16, 777 (1977).CrossRefGoogle Scholar
  15. 15.
    V.I. Karpman and E.M. Maslov, Phys. Letters 60A, 307 (1977).Google Scholar
  16. 16.
    D.J. Kaup and A.C. Newell, Proc. Roy. Soc. London A361, 413 (1978).CrossRefGoogle Scholar
  17. 17.
    K. Druhl, R.G. Wenzel, and J.L. Caristen. Phys. Rev. Lett. 51 1171 (1983).Google Scholar
  18. 18.
    J.L. Caristen, R.G. Wenzel, and K. Druhl, SPIE 380, 201 (1983).CrossRefGoogle Scholar
  19. 19.
    H. Steudel, Physics 6D, 155 (1983).Google Scholar
  20. 20.
    D.J. Kaup, Physics 6D, 143 (1983).Google Scholar
  21. 21.
    F.Y.F. Chu and A.C. Scott, Phys. Rev. Al2, 2060 (1975).Google Scholar
  22. 22.
    D.J. Kaup, ‘Using Dissipation for Creating Solitons’, (Preprint in Preparation).Google Scholar
  23. 23.
    R.G. Wenzel (private communication).Google Scholar
  24. 24.
    K. Druhl (private communication).Google Scholar
  25. 25.
    D.J. Kaup, Stud. Appl. Math. 59t 25 (1978).Google Scholar
  26. 26.
    G.L. Lamb, Jr.. Phys. Rev. Lett. 31, 196 (1973).CrossRefGoogle Scholar
  27. 27.
    M.J. Ablowitz, D.T. Kaup, and A.C. Newell, J. Math. Phys. 15, 1852 (1974).CrossRefGoogle Scholar
  28. 28.
    D.J. Kaup, Phys. Rev. A16, 704 (1977).CrossRefGoogle Scholar
  29. 29.
    D.B. Nicholson (private communication).Google Scholar
  30. 30.
    A.V. Mikhailov, Pis’ma Zh. Eksp. Teor. Fiz. 23, 356 (1976).Google Scholar
  31. A.V. Mikhailov, Sov. Phys.-JETP Lett. 23, 320 (1976).Google Scholar
  32. 31.
    D.J. Kaup and A.C. Newell, Lett. al Nuovo Cimento 20, 325 (1977).CrossRefGoogle Scholar
  33. 32.
    D.J. Kaup and A.C. Newell, J. Math. Phys. 19, 798 (1978).CrossRefGoogle Scholar
  34. 33.
    T. Kawata and H. Inoue, J. Phys. Soc. Japan 44, 1968 (1978).CrossRefGoogle Scholar
  35. 34.
    V.S. Gerdzhikov, V.S. Ivanov, and P.P. Kulish, Teor. Math. Fiz. (USSR) 44, 342 (1980)Google Scholar
  36. 34.
    V.S. Gerdzhikov, V.S. Ivanov, and P.P. Kulish, Theor. Math. Phys. (USA) 44, 784 (1980).CrossRefGoogle Scholar
  37. 35.
    B.L. Holian and G.K. Straub, Phys. Rev. B 18, 1593 (1978).CrossRefGoogle Scholar
  38. 36.
    T.G. Hill and L. Knopoff, J. Geophys. Res. 85, 7025 (1980).CrossRefGoogle Scholar
  39. 37.
    D.J. Kaup, J. Math. Phys. 25, 277 (1984).CrossRefGoogle Scholar
  40. 38.
    D.J. Kamp and D.H. Neuberger, J. Math. Phys. 25, 282 (1984).CrossRefGoogle Scholar
  41. 39.
    J.N. Elgin and D.J. Kamp, Optics Comm. 43 233 (1982).CrossRefGoogle Scholar
  42. 40.
    J. Sargent III, M.O. Scully and W.E. Lamb, Laser Physics (Addison Wesley Publishing Co., 1974 ).Google Scholar
  43. 41.
    M. Wadati, J. Phys. Soc. Japan, 52, 2642 (1983).CrossRefGoogle Scholar
  44. 42.
    D.J. Kaup, Phys. Rev. B29, 1072 (1984).Google Scholar
  45. 43.
    D.J. Kaup, Phys. Rev. B27, 6787 (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • D. J. Kaup
    • 1
  1. 1.Department of PhysicsClarkson UniversityPotsdamUSA

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