Global Dynamics Below Excited Solitons for the Non-Radial NLS with Potential

被引：0

作者：

Masaki, Satoshi ^{[1
,2
]}

Murphy, Jason ^{[3
]}

Segata, Jun - ichi ^{[4
]}

机构：

[1] Osaka Univ, Grad Sch Engn Sci, Dept Syst Innovat, Toyonaka, Osaka 5608531, Japan

[2] Hokkaido Univ, Fac Sci, Dept Math, 10-8 Kita Ku, Sapporo 0600810, Japan

[3] Missouri Univ Sci & Technol, Dept Math & Stat, 400 W 12th St, Rolla, MO 65409 USA

[4] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2024年 / 73卷 / 03期

关键词：

NONLINEAR SCHRODINGER-EQUATIONS; ASYMPTOTIC STABILITY; WAVE-OPERATORS; WELL-POSEDNESS; ENERGY SPACE; BLOW-UP; SCATTERING;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the global dynamics of solutions to the 3d cubic nonlinear Schrodinger equation in the presence of an external potential, in the setting in which the equation admits both ground state solitons and excited solitons at small mass. We prove that small mass solutions with energy below that of the excited solitons either scatter to the ground states or grow their H-1-norm in time. In particular, we give an extension of the result of Nakanishi [30] from the radial to the non-radial setting.

引用

页码：1097 / 1205

页数：109

共 42 条

[1] Blowup and scattering problems for the nonlinear Schrodinger equations [J].