带势的非线性薛定谔方程在激发孤子以下的全局动力学
偏微分方程分析
2016-02-11 v2
摘要
考虑具有单个负本征值势的非线性薛定谔方程(NLS)。它具有负小能量的孤子，它们是渐近稳定的；若非线性为聚焦型，则还具有正大能量的孤子，它们是不稳定的。本文在小质量和径向对称性约束下，对孤子第二低能量以下的全局动力学进行分类。
引用
@article{arxiv.1504.06532,
title = {Global dynamics below excited solitons for the nonlinear Schr\"odinger equation with a potential},
author = {Kenji Nakanishi},
journal= {arXiv preprint arXiv:1504.06532},
year = {2016}
}
备注
43 pages. A gap has been fixed in Section 8 in the case of two non-scattering profiles, with Lemma 7.1 modified and a more general statement (Theorem 7.2)