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Remarks on the Scattering problem for nonlinear Schrödinger equations

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Differential Equations and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

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References

  1. J. E. Barab, Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation, J. Math. Phys., 25 (1984), 3270–3273.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. C. Dong and S. Li, On the initial value problem for a nonlinear Schrödinger equation, J. Diff. Eqs., 42 (1981), 353–365.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I: The Cauchy problem, J. Funct. Anal., 32 (1979), 1–32.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Ginibre and G. Velo, On a class of nonlinear SchrÖdinger equations. II: Scattering theory, J. Funct. Anal., 32 (1979), 33–71.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Ginibre and G. Velo, Sur une équation de Schrödinger non linéaire avec interaction non locale, in “Nonlinear parial differential equations and their applications”, College de France Seminair, Vol. II, Pitman, Boston, 1981.

    Google Scholar 

  6. J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations, J. Math. Pur. Appl., 64 (1985), 363–401.

    MathSciNet  MATH  Google Scholar 

  7. J. Ginibre and G. Velo, Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations, Ann. I. H. P. (Phys. Theor.), 43 (1985), 399–442.

    MathSciNet  MATH  Google Scholar 

  8. N. Hayashi and M. Tsutsumi, L∞ (ℝn)-decay of classical solutions for nonlinear Schrödinger equations, to appear.

    Google Scholar 

  9. N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations, to appear in J. Funct. Anal.

    Google Scholar 

  10. W. Hunziker, On the space-time behavior of Schrödinger wavefunctions, J. Math. Phys., 7 (1966), 300–304.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Jensen, Commutator methods and a smooth property of the Schrödinger evolution group, Math. Z., 191 (1986), 53–59.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. E. Lin and W. A. Strauss, Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal., 30 (1978), 245–263.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Reed. Abstract nonlinear wave equations, Lecture Notes in Math., 507, Springer-Verlag, Berli-Heidelberg-New York, 1976.

    Book  MATH  Google Scholar 

  14. W. A. Strauss, Everywhere defined wave operators, in “Nonlinear Evolution Equations”, pp. 85–102, Academic Press, New York, 1978.

    Google Scholar 

  15. W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal., 41 (1981), 110–133.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44 (1977), 705–714.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Tsutsumi, Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor thesis, University of Tokyo, 1985.

    Google Scholar 

  18. Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations, Ann. I. H. P. (Phys. Theor.), 43 (1985), 321–347.

    MathSciNet  MATH  Google Scholar 

  19. Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations, Bull. (New Series) Amer. Math. Soc., 11 (1984), 186–188.

    Article  MathSciNet  MATH  Google Scholar 

  20. K. Yajima, The surfboard Schrödinger equations, Comm. Math. Phys., 96 (1984), 349–360.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Physics, Waseda University, 160, Tokyo, Japan

    Nakao Hayashi

  2. Faculty of Integrated Arts and Sciences, Hiroshima University, 730, Hiroshima, Japan

    Yoshio Tsutsumi

Authors
  1. Nakao Hayashi
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  2. Yoshio Tsutsumi
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Editor information

Ian W. Knowles Yoshimi Saitō

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© 1987 Springer-Verlag

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Hayashi, N., Tsutsumi, Y. (1987). Remarks on the Scattering problem for nonlinear Schrödinger equations. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080593

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  • DOI: https://doi.org/10.1007/BFb0080593

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

  • eBook Packages: Springer Book Archive

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