Bifurcations of Standing Localized Waves on Periodic Graphs
Bifurcations of Standing Localized Waves on Periodic Graphs
复制标题
周期图上驻波的分岔
DOI：
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复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. Schneider
中科院分区：
文献类型：
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作者：
D. Pelinovsky;G. Schneider
研究了周期图上的非线性薛定谔方程在Kirchhoff边界条件下的解.利用双曲不动点附近二维离散映射的分析，研究了定常薛定谔方程线性谱底部以下频率的定常局域驻波的分岔。我们证明了存在两个不同的家庭的小振幅驻波局域波，这是对称的两个对称点的周期图。我们还证明了这两个家庭的性质，特别是，积极性和指数衰减。在周期图上的NLS方程均匀化的背景下，讨论了二维离散映射到无穷直线上的定常NLS方程的渐近约化。
The nonlinear Schrödinger (NLS) equation is considered on a periodic graph subject to the Kirchhoff boundary conditions. Bifurcations of standing localized waves for frequencies lying below the bottom of the linear spectrum of the associated stationary Schrödinger equation are considered by using analysis of two-dimensional discrete maps near hyperbolic fixed points. We prove the existence of two distinct families of small-amplitude standing localized waves, which are symmetric about the two symmetry points of the periodic graph. We also prove properties of the two families, in particular, positivity and exponential decay. The asymptotic reduction of the two-dimensional discrete map to the stationary NLS equation on an infinite line is discussed in the context of the homogenization of the NLS equation on the periodic graph.
具有周期势的非线性椭圆问题格方程的证明
影响因子：
2.4
作者：
Pelinovsky D
通讯作者：
Pelinovsky D
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