On stability properties of the Cubic-Quintic Schródinger equation with \begin{document}$\delta$\end{document}-point interaction
On stability properties of the Cubic-Quintic Schródinger equation with \begin{document}$\delta$\end{document}-point interaction
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具有egin{document}$delta$end{document}点相互作用的三次五次薛定谔方程的稳定性性质
DOI：
10.3934/cpaa.2019094
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发表时间：
2019
影响因子：
1
通讯作者：
César A. Hernández Melo
中科院分区：
文献类型：
--
作者：
J. Pava;César A. Hernández Melo
本文研究了具有由Dirac增量决定的点相互作用的五阶非线性Schrodinger方程的峰值驻波解的存在性和轨道稳定性。我们研究吸引-吸引和吸引-排斥非线性的情况，我们恢复了文献中的一些结果。通过扰动方法和连续的参数，我们确定的莫尔斯指数的一些特定的自伴算子的稳定性研究中出现的。从光谱不稳定性的结果建立轨道不稳定性的影响。在吸引-吸引情形和聚焦相互作用情形下，我们给出了一种基于对称算子扩张理论的确定莫尔斯指数的方法.
We study analytically and numerically the existence and orbital stability of the peak-standing-wave solutions for the cubic-quintic nonlinear Schrodinger equation with a point interaction determined by the delta of Dirac. We study the cases of attractive-attractive and attractive-repulsive nonlinearities and we recover some results in the literature. Via a perturbation method and continuation argument we determine the Morse index of some specific self-adjoint operators that arise in the stability study. Orbital instability implications from a spectral instability result are established. In the case of an attractive-attractive case and an focusing interaction we give an approach based in the extension theory of symmetric operators for determining the Morse index.