On the standing waves of the NLS-log equation with point interaction on a star graph

Nataliia Goloshchapova

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arXiv · 1803.07194

On the standing waves of the NLS-log equation with point interaction on a star graph

Nataliia Goloshchapova

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Abstract

We study a nonlinear Schr\"odinger equation with logarithmic nonlinearity on a star graph $\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\in \mathbb{R}$. We investigate orbital stability and spectral instability of the standing wave solutions $e^{i\omega t}\mathbf{\Phi}(x)$ to the equation when the profile $\mathbf\Phi(x)$ has mixed structure (i.e. has bumps and tails). In our approach we essentially use the extension theory of symmetric operators by Krein - von Neumann, and the analytic perturbations theory.

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BibTeX RIS

Nataliia Goloshchapova. 2018-03-19. On the standing waves of the NLS-log equation with point interaction on a star graph. https://arxiv.org/abs/1803.07194

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