MODIFIED WAVE OPERATORS FOR NONLINEAR SCHR¨ ODINGER EQUATIONS IN ONE AND TWO DIMENSIONS
MODIFIED WAVE OPERATORS FOR NONLINEAR SCHR¨ ODINGER EQUATIONS IN ONE AND TWO DIMENSIONS
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发表时间：
2004
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通讯作者：
N. Hayashi;P. Naumkin;A. Shimomura;S. Tonegawa
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作者：
N. Hayashi;P. Naumkin;A. Shimomura;S. Tonegawa
我们研究一维或二维空间中具有三次和二次非线性的非线性薛定谔方程解的渐近行为，特别是散射理论。非线性是规范不变项和非规范不变项的总和。这些方程的散射问题属于长程情况。我们针对最终的小数据证明了这些方程的修正波算子的存在性。我们的结果是对之前工作（13）的改进。
We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrodinger equations with cubic and qua- dratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scat- tering 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).