Scattering problem for nonlinear Schrödinger equations
Annales de l'I.H.P. Physique théorique, Volume 43 (1985) no. 3, p. 321-347
@article{AIHPA_1985__43_3_321_0,
     author = {Tsutsumi, Yoshio},
     title = {Scattering problem for nonlinear Schr\"odinger equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {43},
     number = {3},
     year = {1985},
     pages = {321-347},
     zbl = {0612.35104},
     mrnumber = {824843},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1985__43_3_321_0}
}
Tsutsumi, Yoshio. Scattering problem for nonlinear Schrödinger equations. Annales de l'I.H.P. Physique théorique, Volume 43 (1985) no. 3, pp. 321-347. http://www.numdam.org/item/AIHPA_1985__43_3_321_0/

[1] J.E. Barab, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., t. 25, 1984, p. 3270-3273. | MR 761850 | Zbl 0554.35123

[2] J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, Berlin/Heidelberg/New York, 1976. | MR 482275 | Zbl 0344.46071

[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. | MR 744828 | Zbl 0524.35084

[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. | MR 639226 | Zbl 0475.35036

[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. | MR 533219 | Zbl 0396.35028

[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. | MR 533219 | Zbl 0396.35029

[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. | MR 652511 | Zbl 0497.35024

[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. | MR 741079 | Zbl 0593.35078

[9] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations, preprint.

[10] N. Hayashi and M. Tsutsumi, L∞-decay of classical solutions for nonlinear Schrödinger equations, in preparation.

[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. | MR 515228 | Zbl 0395.35070

[12] H. Pecher, Decay of solutions of nonlinear wave equations in three space dimensions, J. Funct. Anal., t. 46, 1982, p. 221-229. | MR 660186 | Zbl 0482.35057

[13] H. Pecher, Decay and asymptotics for higher dimensional nonlinear wave equations. J. Diff. Eqs., t. 46, 1982, p. 103-151. | MR 677586 | Zbl 0465.35065

[14] M. Reed, Abstract nonlinear wave equations, Lecture Notes in Math., t. 507, Springer-Verlag, Berlin, Heidelberg, New York, 1976. | Zbl 0317.35002

[15] M. Reed and B. Simon, Method of Modern Mathematical Physics, Vol. II. Fourier Analysis and Self-adjointness, Academic Press, New York, 1975. | Zbl 0308.47002

[16] W.A. Strauss, Everywhere defined wave operators, in Nonlinear Evolution Equations, p. 85-102, Academic Press, New York, 1978. | MR 513813 | Zbl 0466.47005

[17] W.A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal., t. 41, 1981, p. 110-133. | MR 614228 | Zbl 0466.47006

[18] W.A. Strauss, Nonlinear scattering theory at low energy: sequel, J. Funct. Anal., t. 43, 1981, p. 281-293. | MR 636702 | Zbl 0494.35068

[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. | MR 512086 | Zbl 0372.35001

[20] M. Tsutsumi and N. Hayashi, Classical solutions of nonlinear Schrödinger equations in higher dimensions, Math. Z., t, 177, 1981, p. 217-234. | MR 612876 | Zbl 0438.35028

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

[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. | MR 741737 | Zbl 0555.35028

[23] K. Yajima, The surfboard Schrödinger equations, Comm. Math. Phys., t. 96, 1984, p. 349-360. | MR 769352 | Zbl 0599.35037