Mass-constrained ground states of the stationary NLSE on periodic metric graphs
Mass-constrained ground states of the stationary NLSE on periodic metric graphs
复制标题
周期度量图上静止 NLSE 的质量约束基态
DOI：
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Simone Dovetta
中科院分区：
文献类型：
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作者：
Simone Dovetta
We investigate the existence of ground states with fixed mass for the nonlinear Schrödinger equation with a pure power nonlinearity on periodic metric graphs. Within a variational framework, both the L2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2$$end{document}-subcritical and critical regimes are studied. In the former case, we establish the existence of global minimizers of the NLS energy for every mass and every periodic graph. In the critical regime, a complete topological characterization is derived, providing conditions which allow or prevent ground states of a certain mass from existing. Besides, a rigorous notion of periodic graph is introduced and discussed.
We investigate the existence of ground states with fixed mass for the nonlinear Schrödinger equation with a pure power nonlinearity on periodic metric graphs. Within a variational framework, both the L2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2$$end{document}-subcritical and critical regimes are studied. In the former case, we establish the existence of global minimizers of the NLS energy for every mass and every periodic graph. In the critical regime, a complete topological characterization is derived, providing conditions which allow or prevent ground states of a certain mass from existing. Besides, a rigorous notion of periodic graph is introduced and discussed.
周期量子图 NLS 近似的有效性
DOI：
10.1007/s00030-016-0417-7
发表时间：
2016
期刊：
Nonlinear Differential Equations and Applications NoDEA
影响因子：
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作者：
S. Gilg;D. Pelinovsky;G. Schneider
通讯作者：
G. Schneider