Scattering solutions to nonlinear Schrodinger equation with a long range potential

被引：0

作者：

Hamano, Masaru ^{[1
]}

Ikeda, Masahiro ^{[2
,3
]}

机构：

[1] Waseda Univ, Fac Sci & Engn, 3-4-1 Okubo,Shinjuku Ku, Tokyo 1698555, Japan

[2] Keio Univ, Fac Sci & Technol, Dept Math, 3-14-1 Hiyoshi,Kohoku Ku, Yokohama 2238522, Japan

[3] Riken, Ctr Adv Intelligence Project, Tokyo, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 528卷 / 01期

基金：

日本学术振兴会;

关键词：

Nonlinear Schrodinger equation; Long range potential; Scattering; GLOBAL WELL-POSEDNESS; BLOW-UP; NLS;

D O I：

10.1016/j.jmaa.2023.127468

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a nonlinear Schrodinger equation with a repulsive inverse power potential. It is known that the corresponding stationary problem has a "radial" ground state. Here, the "radial" ground state is a least energy solution among radial solutions to the stationary problem. We prove that if radial initial data below the "radial" ground state has positive virial functional, then the corresponding solution to the nonlinear Schrodinger equation scatters. In particular, we can treat not only short range potentials but also long range potentials. & COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：36

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