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Determining the final profiles from the initial profiles for the full three-dimensional three-wave resonant interaction

  • D. J. Kaup
Inverse Scattering Theory and Related Topics
Part of the Lecture Notes in Physics book series (LNP, volume 130)

Keywords

Fundamental Solution Asymptotic Form Inverse Scattering Scattering Problem Resonant Interaction 
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References

  1. [1]
    H. Cornille: J. Math. Phys. 20, 1653 (1979)Google Scholar
  2. [2]
    D.J. Kaup: “A method for solving the separable initial value problem of the full three-dimensional threewave resonant interaction”, to appear in Stud. Appl. Math.Google Scholar
  3. [3]
    D.J. Kaup: Stud. Appl. Math. 55, 9 (1976)Google Scholar
  4. [4]
    V.E. Zakharov, S.V. Manakov: Zh. Eksp. Teor. Fiz. 69, 1654 (1975) [Sov. Phys.-JETP 42, 842 (1976)]Google Scholar
  5. [5]
    D.J. Kaup, A.H. Reiman, A. Bets: Rev. Mod. Phys. 51, 275 (1979)Google Scholar
  6. [6]
    M.J. Ablowitz, R. Haberman: J. Math. Phys. 16, 2301 (1975)Google Scholar
  7. [7]
    V.E. Zakharov, A.B. Shabat: Funk. Anal. Priloz. 8, 43 (1974)Google Scholar
  8. [8]
    D.J. Kaup: “The inverse scattering solution for the full three-dimensional three-wave resonant interaction,” to appear in Physica D.Google Scholar
  9. [9]
    Parts of this two-dimensional inverse scattering problem have also been solved by L.P. Niznik: Inverse Nonstationary Problem of Scattering Theory (Naukora Dumka, Kiev, 1973), 182 pp.Google Scholar
  10. [10]
    D.J. Kaup: “The solution of the general initial value problem for the full three-dimensional three-wave resonant interaction,” to appear in the proceedings of the Soviet-American Soliton Symposium, Kiev, September 2–14, 1979Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • D. J. Kaup
    • 1
  1. 1.Department of PhysicsClarkson College of TechnologyPotsdam

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