Scattering problem for nonlinear Schrödinger equations
Annales de l'I.H.P. Physique théorique, Tome 43 (1985) no. 3, pp. 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},
     pages = {321--347},
     publisher = {Gauthier-Villars},
     volume = {43},
     number = {3},
     year = {1985},
     mrnumber = {824843},
     zbl = {0612.35104},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1985__43_3_321_0/}
}
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Tsutsumi, Yoshio. Scattering problem for nonlinear Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) no. 3, pp. 321-347. http://archive.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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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

[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 | Zbl

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

[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 | Zbl

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