Remarks on long range scattering for nonlinear Schrödinger equations with Stark effects
Remarks on long range scattering for nonlinear Schrödinger equations with Stark effects
复制标题
DOI：
10.1215/kjm/1250282974
复制
发表时间：
2005
影响因子：
--
通讯作者：
A. Shimomura;S. Tonegawa
中科院分区：
文献类型：
--
作者：
A. Shimomura;S. Tonegawa
本文研究了一类带Stark效应的非线性Schr？dinger方程在一维和二维空间中整体解的存在性和时间渐近性态.在一维和二维情况下，非线性分别是三次和二次的，它是规范不变项和非规范不变项的总和。这种非线性在近距离散射和远距离散射之间是关键的。对于小的最终态，构造了该方程的修正的艾德波算子。它的定义域是H2 <$FH2中的某个小球，其中F是傅里叶变换。
In this paper, the global existence and asymptotic behavior in time of solutions for the nonlinear Schr¨odinger equation with the Stark effect in one or two space dimensions are studied. The nonlinearity is cubic and quadratic in one and two dimensional cases, respectively, and it is a summation of a gauge invariant term and non-gauge invariant terms. This nonlinearity is critical between the short range scattering and the long range one. A modified wave operator to this equation is constructed for small final states. Its domain is a certain small ball in H 2 ∩ F H 2 , where F is the Fourier transform.