We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrödinger 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 .
|Number of pages||16|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 2004 Apr 21|
- Modified wave operators
- Nonlinear Schrödinger equations
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