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

Date

2004-04-21

Authors

Hayashi, Nakao
Naumkin, Pavel I.
Shimomura, Akihiro
Tonegawa, Satoshi

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

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].

Description

Keywords

Modified wave operators, Nonlinear Schrodinger equations

Citation

Hayashi, N., Naumkin, P. I., Shimomura, A., & Tonegawa, S. (2004). Modified wave operators for nonlinear Schrodinger equations in one and two dimensions. <i>Electronic Journal of Differential Equations, 2004</i>(62), pp. 1-16.

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Attribution 4.0 International

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