论文标题
NLSE的散射失败，二和三维的点相互作用
Failure of scattering for the NLSE with a point interaction in dimension two and three
论文作者
论文摘要
在本文中，我们考虑了二维和三个方面的功率非线性和点相互作用（物理文献中的$δ$ - 优势”）的NLS方程。我们将证明，对于低功率非线性，将散射到自由动力学或站立波浪中。在最近的论文中，墨菲和中尼尼考虑了具有电势和措施的NLS方程，足以包括尺寸一$δ$ - 电位，它们显示出类似的性质。在这方面，我们的贡献是扩展到更高维度的扩展，并且需要对相互作用的线性部分进行不同的处理，这是由于所涉及的奇异性的质量不同和更强的特征。
In this paper we consider the NLS equation with power nonlinearity and a point interaction (a "$δ$-potential" in the physical literature) in dimension two and three. We will show that for low power nonlinearities there is failure of scattering to the free dynamics or to standing waves. In the recent paper Murphy and Nakanishi consider the NLS equation with potentials and measures, singular enough to include the $δ$-potential in dimension one and they show analogous properties. In this respect our contribution is an extension to higher dimension and it needs a different treatment of the linear part of the interaction, due the qualitatively different and stronger character of the singularity involved.
