On a Class of non Linear Schrödinger Equations with non Local Interaction.

作者: Jean Ginibre , Giorgio Velo

DOI: 10.1007/BF01214768

关键词:

摘要: As regards the first question we prove existence and uniqueness of solutions Cauchy problem with finite initial time; as second one, infinite time, which implies wave operators, asymptotic completeness for a class repulsive interactions. The main reason this investigation is that Eq. (0.1) can be considered classical limit, in field sense, equation describing

参考文章(7)
Avner Friedman, Partial differential equations ,(1969)
Hartmut Pecher, Time dependent nonlinear Schrödinger equations Manuscripta Mathematica. ,vol. 27, pp. 125- 157 ,(1979) , 10.1007/BF01299292
J. M. Chadam, R. T. Glassey, Global existence of solutions to the Cauchy problem for time‐dependent Hartree equations Journal of Mathematical Physics. ,vol. 16, pp. 1122- 1130 ,(1975) , 10.1063/1.522642
A. Bove, G. Da Prato, G. Fano, An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction Communications in Mathematical Physics. ,vol. 37, pp. 183- 191 ,(1974) , 10.1007/BF01646344
J. Ginibre, G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case Journal of Functional Analysis. ,vol. 32, pp. 1- 32 ,(1979) , 10.1016/0022-1236(79)90076-4
J. Ginibre, G. Velo, The classical field limit of scattering theory for non-relativistic many-boson systems. II Communications in Mathematical Physics. ,vol. 66, pp. 37- 76 ,(1979) , 10.1007/BF01562541
Jeng-Eng Lin, Walter A. Strauss, Decay and scattering of solutions of a nonlinear Schrödinger equation Journal of Functional Analysis. ,vol. 30, pp. 245- 263 ,(1978) , 10.1016/0022-1236(78)90073-3