@article{AIHPA_1987__46_2_187_0, author = {Hayashi, Nakao and Tsutsumi, Yoshio}, title = {Scattering theory for {Hartree} type equations}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {187--213}, publisher = {Gauthier-Villars}, volume = {46}, number = {2}, year = {1987}, mrnumber = {887147}, zbl = {0634.35059}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1987__46_2_187_0/} }
TY - JOUR AU - Hayashi, Nakao AU - Tsutsumi, Yoshio TI - Scattering theory for Hartree type equations JO - Annales de l'I.H.P. Physique théorique PY - 1987 SP - 187 EP - 213 VL - 46 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1987__46_2_187_0/ LA - en ID - AIHPA_1987__46_2_187_0 ER -
Hayashi, Nakao; Tsutsumi, Yoshio. Scattering theory for Hartree type equations. Annales de l'I.H.P. Physique théorique, Tome 46 (1987) no. 2, pp. 187-213. http://www.numdam.org/item/AIHPA_1987__46_2_187_0/
[1] Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation. J. Math. Phys., t. 25, 1984, p. 3270-3273. | MR | Zbl
,[2] On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations. Math. Z., t. 186, 1984, p. 383-391. | MR | Zbl
,[3] On scattering and everywhere defined scattering operators for non-linear Klein-Gordon equations. J. Differential Equations, t. 56, 1985, p. 310-344. | MR | Zbl
,[4] Global existence of solutions to the Cauchy problem for time dependent Hartree equations. J. Math. Phys., t. 16, 1975, p. 1122-1130. | MR | Zbl
and ,[5] Partial Differential Equations. Holt-Rinehart and Winston, New York, 1969. | MR | Zbl
,[6] On a class of nonlinear Schrödinger equation I, II. J. Funct. Anal, t. 32, 1979, p. 1-32, 33-71 ; III, Ann. Inst. Henri Poincaré, Physique Théorique, t. 28, 1978, p. 287-316. | Numdam | MR | Zbl
and ,[7] On a class of nonlinear Schrödinger equations with non local interactin. Math. Z., t. 170, 1980, p. 109-136. | MR | Zbl
and ,[8] Sur une équation de Schrödinger non linéaire avec interaction non locale, in Nonlinear partial differential equations and their applications. Collège de France, Séminaire, vol. II, Pitman, Boston, 1981. | MR | Zbl
and ,[9] Scattering theory in the energy space for a class of non-linear Schrödinger equations, J. Math. pures et appl., t. 64, 1985, p. 363-401. | MR | Zbl
and ,[10] Asymptotic behavior of solutions to a certain nonlinear-Hartree equations, Comm. Math. Phys., t. 53, 1977, p. 9-18. | MR | Zbl
,[11] L∞-decay of classical solutions for nonlinear Schrödinger equations, preprint.
and ,[12] On solutions of the initial value problem for the nonlinear Schrödinger equations, to appear in J. Funct. Anal. | MR | Zbl
, and ,[13] Remarks on the scattering problem for nonlinear Schrödinger equations, preprint. | MR
and ,[14] On the space-time behavior of Schrödinger wavefunctions. J. Math. Phys., t. 7, 1965, p. 300-304. | MR | Zbl
,[15] Commutator methods and a smoothing property of the Schrödinger evolution group. Math. Z., t. 191, 1986, p. 53-59. | MR | Zbl
,[16] Singular Integral and Differentiability Properties of Functions, Princeton Univ. Press. Princeton Math. Series 30, 1970. | MR | Zbl
,[17] Nonlinear invariant wave equations, in Invariant Wave Equations (Erice, 1977), Lecture Notes in Physics, t. 78, Springer-Verlag, Berlin-Heidelberg- New York, 1978, p. 197-249. | MR
,[18] Nonlinear scattering theory at low energy. J. Funct. Anal., t. 41, 1981, p. 110-133. | MR | Zbl
,[19] Nonlinear Scattering theory at low energy: Sequel. J. Funct. Anal., t. 43, p. 281-293, | MR | Zbl
,[20] 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
,[21] Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor Thesis, Univ. of Tokyo, 1985.
,[22] Scattering problem for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 43, 1985, p. 321-347. | Numdam | MR | Zbl
,[23] The asymptotic behavior of nonlinear Schrödinger equations, Bull. (New Series). Amer. Math. Soc., t. 11, 1984, p. 186-188. | MR | Zbl
and ,[24] The surfboard Schrödinger equations. Comm. Math. Phys., t. 96, 1984, p. 349-360. | MR | Zbl
,[25] Private communication.
,[26] On nonlinear Schrödinger equations, preprint, University of California, Berkeley, 1986. | MR
,[27] L2-solutions for nonlinear Schrödinger equations and nonlinear groups, to appear in Funkcialaj Ekvacioj. | MR | Zbl
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