Scattering problem for nonlinear Schrödinger equations

Yoshio Tsutsumi

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 43, Issue: 3, page 321-347
  • ISSN: 0246-0211

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Tsutsumi, Yoshio. "Scattering problem for nonlinear Schrödinger equations." Annales de l'I.H.P. Physique théorique 43.3 (1985): 321-347. <http://eudml.org/doc/76303>.

@article{Tsutsumi1985,
author = {Tsutsumi, Yoshio},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {nonlinear Schrödinger equation; asymptotic behavior; wave operator; asymptotic completeness; Strichartz estimate; transformation},
language = {eng},
number = {3},
pages = {321-347},
publisher = {Gauthier-Villars},
title = {Scattering problem for nonlinear Schrödinger equations},
url = {http://eudml.org/doc/76303},
volume = {43},
year = {1985},
}

TY - JOUR
AU - Tsutsumi, Yoshio
TI - Scattering problem for nonlinear Schrödinger equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 43
IS - 3
SP - 321
EP - 347
LA - eng
KW - nonlinear Schrödinger equation; asymptotic behavior; wave operator; asymptotic completeness; Strichartz estimate; transformation
UR - http://eudml.org/doc/76303
ER -

References

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  1. [1] J.E. Barab, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., t. 25, 1984, p. 3270-3273. Zbl0554.35123MR761850
  2. [2] J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, Berlin/Heidelberg/New York, 1976. Zbl0344.46071MR482275
  3. [3] P. Brenner, On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations, Math. Z., t. 186, 1984, p. 383-391. Zbl0524.35084MR744828
  4. [4] G.C. Dong and S. Li, On the initial value problem for a nonlinear Schrödinger equation, J. Diff. Eqs., t. 42, 1981, 353-365. Zbl0475.35036MR639226
  5. [5] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, J. Funct. Anal., t. 32, 1979, p. 1-32. Zbl0396.35028MR533219
  6. [6] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. II. Scattering theory, J. Funct. Anal., t. 32, 1979, p. 33-71. Zbl0396.35029MR533219
  7. [7] J. Ginibre and G. Velo, Sur une équation de Schrödinger non linéaire avec interaction non locale, in Nonlinear partial differential equations and their applications, College de France Seminair, Vol. II, Pitman, Boston, 1981. Zbl0497.35024MR652511
  8. [8] J. Ginibre and G. Velo, Théorie de la diffusion dans l'espace d'énergie pour une classe d'équations de Schrödinger non linéaire, C. R. Acad. Sci. Paris, t. 298, 1984, p. 137-140. Zbl0593.35078MR741079
  9. [9] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations, preprint. Zbl0626.35073
  10. [10] N. Hayashi and M. Tsutsumi, L∞-decay of classical solutions for nonlinear Schrödinger equations, in preparation. Zbl0651.35014
  11. [11] J.E. Lin and W.A. Strauss, Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal., t. 30, 1978, p. 245-263. Zbl0395.35070MR515228
  12. [12] H. Pecher, Decay of solutions of nonlinear wave equations in three space dimensions, J. Funct. Anal., t. 46, 1982, p. 221-229. Zbl0482.35057MR660186
  13. [13] H. Pecher, Decay and asymptotics for higher dimensional nonlinear wave equations. J. Diff. Eqs., t. 46, 1982, p. 103-151. Zbl0465.35065MR677586
  14. [14] M. Reed, Abstract nonlinear wave equations, Lecture Notes in Math., t. 507, Springer-Verlag, Berlin, Heidelberg, New York, 1976. Zbl0317.35002
  15. [15] M. Reed and B. Simon, Method of Modern Mathematical Physics, Vol. II. Fourier Analysis and Self-adjointness, Academic Press, New York, 1975. Zbl0308.47002
  16. [16] W.A. Strauss, Everywhere defined wave operators, in Nonlinear Evolution Equations, p. 85-102, Academic Press, New York, 1978. Zbl0466.47005MR513813
  17. [17] W.A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal., t. 41, 1981, p. 110-133. Zbl0466.47006MR614228
  18. [18] W.A. Strauss, Nonlinear scattering theory at low energy: sequel, J. Funct. Anal., t. 43, 1981, p. 281-293. Zbl0494.35068MR636702
  19. [19] R.S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., t. 44, 1977, p. 705-714. Zbl0372.35001MR512086
  20. [20] M. Tsutsumi and N. Hayashi, Classical solutions of nonlinear Schrödinger equations in higher dimensions, Math. Z., t, 177, 1981, p. 217-234. Zbl0438.35028MR612876
  21. [21] Y. Tsutsumi, Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor thesis, University of Tokyo, 1985. 
  22. [22] Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations, Bull. (New Series), Amer. Math. Soc., t. 11, 1984, p. 186-188. Zbl0555.35028MR741737
  23. [23] K. Yajima, The surfboard Schrödinger equations, Comm. Math. Phys., t. 96, 1984, p. 349-360. Zbl0599.35037MR769352

Citations in EuDML Documents

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  1. J. Ginibre, G. Velo, Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations
  2. Nakao Hayashi, Pavel I. Naumkin, Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation
  3. J. Ginibre, T. Ozawa, G. Velo, On the existence of the wave operators for a class of nonlinear Schrödinger equations
  4. Nakao Hayashi, Tohru Ozawa, Scattering theory in the weighted L 2 ( n ) spaces for some Schrödinger equations
  5. J. Ginibre, G. Velo, Conformal invariance and time decay for non linear wave equations. I
  6. Nakao Hayashi, Yoshio Tsutsumi, Scattering theory for Hartree type equations
  7. Jean Ginibre, Théorie de la diffusion pour des équations semi linéaires

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