Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 62, pp. 1-16.

Title: Modified wave operators for nonlinear Schrodinger equations in
       one and two dimensions

Authors: Nakao Hayashi (Osaka Univ., Japan)
         Pavel I. Naumkin (UNAM Campus Morelia, Mexico)
         Akihiro Shimomura (Gakushuin Univ., Tokyo, Japan)
	 Satoshi Tonegawa (Nihon Univ., Tokyo, Japan)

Abstract:
  We study the asymptotic behavior of solutions, in particular  
  the scattering theory, for the nonlinear Schr\"{o}dinger 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]

Submitted March 10, 2004. Published April 21, 2004.
Math Subject Classifications: 35Q55, 35B40, 35B38
Key Words: Modified wave operators; nonlinear Schrodinger equations