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Existence of solutions and scattering theory for the non linear schrödinger equation

  • J. Ginibre
  • G. Velo
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 120)

Keywords

Cauchy Problem Wave Operator Dispersive Solution Asymptotic Completeness Free 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]
    Baillon, J.B., Cazenave, T., Figueira, M., C.R.Acad.Sc.Paris, 284, 869–872, (1977).Google Scholar
  2. [2]
    Bove, A., Da Prato, G., Fano, G., Comm.Math.Phys., 37, 183–191, (1974), Comm.Math.Phys. 49, 25–33, (1976).Google Scholar
  3. [3]
    Bresiz, H., Gallouet, T., Nonlinear Schrödinger evolution equations, preprint 1979.Google Scholar
  4. [4]
    Cazenave, T., Haraux, A., C.R.Acad.Sc.Paris, 288, 253–256, (1979).Google Scholar
  5. [5]
    Chadam, J.M., Glassey, R.T., J.Math.Phys., 16, 1122–1130, (1975).Google Scholar
  6. [6]
    Davies, E.B., Some time dependent Hartree equations, preprint 1979.Google Scholar
  7. [7]
    Gelfand, I.M., Dikii, L.A., Russian Math.Surveys, 30, 77–113, (1975), (Transl.from Usp.Mat.Nauk 30, 67–100, (1975)).Google Scholar
  8. [8]
    Ginibre, J., Velo, G., J.Func.Anal., 32, 1–32, (1979); J.Func.Anal., 32, 33–71, (1979); Ann.Inst.H.Poincaré, 28, 287–316, (1978).Google Scholar
  9. [9]
    Ginibre, J., Velo, G., C.R.Acad.Sc.Paris, 288, 683–685, (1979); Non linear Schrödinger equations with non local interaction, Mathematische Zeitschrift, in press.Google Scholar
  10. [10]
    Glassey, R.T., J.Math.Phys. 18, 1794–1797, (1977).Google Scholar
  11. [11]
    Lin, J.E., Strauss, W.A., J.Func.Anal., 30, 245–263, (1978).Google Scholar
  12. [12]
    Pecher, H., Von Wahl, W., Time dependent non linear Schrödinger equations, Manuscripta Mathematica, in press.Google Scholar
  13. [13]
    Scott,A.C., Chu, F.Y.F., McLaughlin, D.W., Proc.IEEE, 61, 1443–1483, (1973).Google Scholar
  14. [14]
    Strauss, W.A., Non linear Scattering theory, in Scattering theory in Mathematical Physics, Lavita J.A. and Marchand J. eds., pp.53–78, D.Reidel Publ.Comp., Dordrecht, Holland (1974); Non linear in variant wave equations, in Invariant wave equations, Velo G. and Wightman A.S. eds., pp.197–249, Lecture Notes in Physics 73, Springer Verlag, Berlin-Heidelberg-New York (1978). Reed, M., Abstract non-linear wave equations, Lecture Notes in Mathematics 507, Springer Verlag, Berlin-Heidelberg-New York (1976).Google Scholar
  15. [15]
    Strauss, W.A., The non linear Schrödinger equation, in Contemporary developments in continuum mechanics and partial differential equations, De La Penha G.M. and Medeiras L.A.J. eds., pp.452–465, North Holland Publ.Comp., Amsterdam-New York-Oxford (1978).Google Scholar
  16. [16]
    Zacharov, V.A., Shabat, A.B., Sov.Phys., JETP 34, 62–69 (1972), (Transl.from Zh.Exp.Teor.Fiz. 61, 118–134 (1971)).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Ginibre
    • 1
  • G. Velo
    • 2
  1. 1.Orsay
  2. 2.Bologna

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