@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},
volume = {43},
year = {1985},
pages = {321-347},
mrnumber = {824843},
zbl = {0612.35104},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1985__43_3_321_0}
}
Tsutsumi, Yoshio. Scattering problem for nonlinear Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) pp. 321-347. http://gdmltest.u-ga.fr/item/AIHPA_1985__43_3_321_0/
[1] , 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] and , Interpolation Spaces, Springer-Verlag, Berlin/Heidelberg/New York, 1976. | MR 482275 | Zbl 0344.46071
[3] , 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] and , On the initial value problem for a nonlinear Schrödinger equation, J. Diff. Eqs., t. 42, 1981, 353-365. | MR 639226 | Zbl 0475.35036
[5] and , 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] and , 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] and , 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] and , 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] and , Scattering theory in the energy space for a class of nonlinear Schrödinger equations, preprint.
[10] and , L∞-decay of classical solutions for nonlinear Schrödinger equations, in preparation.
[11] and , 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] , 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] , Decay and asymptotics for higher dimensional nonlinear wave equations. J. Diff. Eqs., t. 46, 1982, p. 103-151. | MR 677586 | Zbl 0465.35065
[14] , Abstract nonlinear wave equations, Lecture Notes in Math., t. 507, Springer-Verlag, Berlin, Heidelberg, New York, 1976. | Zbl 0317.35002
[15] and , Method of Modern Mathematical Physics, Vol. II. Fourier Analysis and Self-adjointness, Academic Press, New York, 1975. | Zbl 0308.47002
[16] , Everywhere defined wave operators, in Nonlinear Evolution Equations, p. 85-102, Academic Press, New York, 1978. | MR 513813 | Zbl 0466.47005
[17] , Nonlinear scattering theory at low energy, J. Funct. Anal., t. 41, 1981, p. 110-133. | MR 614228 | Zbl 0466.47006
[18] , Nonlinear scattering theory at low energy: sequel, J. Funct. Anal., t. 43, 1981, p. 281-293. | MR 636702 | Zbl 0494.35068
[19] , 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] and , Classical solutions of nonlinear Schrödinger equations in higher dimensions, Math. Z., t, 177, 1981, p. 217-234. | MR 612876 | Zbl 0438.35028
[21] , Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor thesis, University of Tokyo, 1985.
[22] and , 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] , The surfboard Schrödinger equations, Comm. Math. Phys., t. 96, 1984, p. 349-360. | MR 769352 | Zbl 0599.35037