度量图上具局域非线性项的非线性薛定谔与狄拉克方程驻波综述
偏微分方程分析
2019-02-06 v1 数学物理
泛函分析
math.MP
摘要
我们简要综述度量图上具局域非线性项的非线性薛定谔方程与非线性狄拉克方程（NLSE/NLDE）驻波的存在性与不存在性。首先关注NLSE，包括亚临界与临界情形，随后关注NLDE，突出其与NLSE的异同。最后，我们展示在非负相对论极限下两方程如何关联，并证明束缚态的收敛性。
引用
@article{arxiv.1901.02696,
title = {An overview on the standing waves of nonlinear Schr\"odinger and Dirac equations on metric graphs with localized nonlinearity},
author = {William Borrelli and Raffaele Carlone and Lorenzo Tentarelli},
journal= {arXiv preprint arXiv:1901.02696},
year = {2019}
}
备注
20 pages, 10 figures; keywords: metric graphs, NLS, NLD, ground states, bound states, localized nonlinearity, nonrelativistic limit