Geodesic
Modified wave operators for nonlinear Schrödinger equations in one and two dimensions
Electronic journal of differential equations, Tome 2004 (2004)
We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrodinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13]
Classification : 35Q55, 35B40, 35B38
Keywords: modified wave operators 
@article{EJDE_2004__2004__a20,
     author = {Hayashi,  Nakao and Naumkin,  Pavel I. and Shimomura,  Akihiro and Tonegawa,  Satoshi},
     title = {Modified wave operators for nonlinear {Schr\"odinger} equations in one and two dimensions},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1064.35188},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a20/}
}
TY  - JOUR
AU  - Hayashi,  Nakao
AU  - Naumkin,  Pavel I.
AU  - Shimomura,  Akihiro
AU  - Tonegawa,  Satoshi
TI  - Modified wave operators for nonlinear Schrödinger equations in one and two dimensions
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a20/
LA  - en
ID  - EJDE_2004__2004__a20
ER  - 
%0 Journal Article
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%A Naumkin,  Pavel I.
%A Shimomura,  Akihiro
%A Tonegawa,  Satoshi
%T Modified wave operators for nonlinear Schrödinger equations in one and two dimensions
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a20/
%G en
%F EJDE_2004__2004__a20
Hayashi,  Nakao; Naumkin,  Pavel I.; Shimomura,  Akihiro; Tonegawa,  Satoshi. Modified wave operators for nonlinear Schrödinger equations in one and two dimensions. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a20/