论文标题
远程散射，用于与时间偿还的谐波电位的关键均匀型非线性schrödinger方程
Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials
论文作者
论文摘要
本文涉及均匀类型非线性schrödinger方程的最终状态问题，并具有时间偿还的谐波潜力。非线性具有关键顺序，不一定是多项式的形式。在量规不变的功率类型的非线性的情况下，第一作者证明了方程式允许一种非平凡的解决方案，该解在[22]中的对数相位校正中表现得像自由解决方案。在本文中，由于Masaki和第二作者提出的傅立叶系列扩展，我们通过该技术将其结果扩展到了总体均质非线性[26]。为了适应上述论文中的论点，我们为繁殖者开发了一个分解身份，并需要更强的衰减条件，以使谐波电位产生的傅立叶系数。此外，在两个或三个维度中，我们改善了[26，28]中最终数据的规律性条件。
This paper is concerned with the final state problem for the homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potential. The nonlinearity has the critical order and is not necessarily the form of a polynomial. In the case of the gauge-invariant power-type nonlinearity, the first author proves that the equation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in [22]. In this paper, we extend his result into the case with the general homogeneous nonlinearity by the technique due to the Fourier series expansion introduced by Masaki and the second author [26]. To adapt the argument in the aforementioned paper, we develop a factorization identity for the propagator and require a little stronger decay condition for the Fourier coefficients arising from the harmonic potential. Moreover, in two or three dimensions, we improve the regularity condition of the final data in [26, 28].
