On Selection of Standing Wave at Small Energy in the 1D Cubic Schr?dinger Equation with a Trapping Potential
On Selection of Standing Wave at Small Energy in the 1D Cubic Schr?dinger Equation with a Trapping Potential
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具有俘获势的一维三次薛定谔方程中小能量驻波的选择
DOI：
10.1007/s00220-022-04487-7
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发表时间：
2022
影响因子：
2.4
通讯作者：
Maeda Masaya
中科院分区：
文献类型：
--
作者：
Cuccagna Scipio;Maeda Masaya
结合Kowalczyk，Martel和Munoz以及Kowalczyk，Martel，Munoz和货车Den Bosch的维里不等式和我们关于如何导出离散模上的非线性诱导耗散的理论，特别是精化剖面的概念，我们展示了如何扩展Kowalczyk，Martel，Munoz和Den Bosch的理论，Munoz和货车Den Bosch的方法应用于当立方NLS中存在大量离散模时的情况，该立方NLS具有与排斥势相关的捕获势，Darboux变换尽管我们的模型通过其非平移不变性避免了平移对波动方程扭结稳定性问题维里不等式影响的一些困难，但它仍然是一个经典模型，并且保留了一些主要困难。
Combining virial inequalities by Kowalczyk, Martel and Munoz and Kowalczyk, Martel, Munoz and Van Den Bosch with our theory on how to derive nonlinear induced dissipation on discrete modes, and in particular the notion of Refined Profile, we show how to extend the theory by Kowalczyk, Martel, Munoz and Van Den Bosch to the case when there is a large number of discrete modes in the cubic NLS with a trapping potential which is associated to a repulsive potential by a series of Darboux transformations. Even though, by its non translation invariance, our model avoids some of the difficulties related to the effect that translation has on virial inequalities of the kink stability problem for wave equations, it still is a classical model and it retains some of the main difficulties.