Standing waves on a flower graph

DOI10.1016/j.jde.2020.09.010zbMath1454.35406arXiv2003.09397OpenAlexW3088040373MaRDI QIDQ2214704

Ke Liang Xiao, Dmitry E. Pelinovsky, Adilbek Kairzhan, Robert Marangell

Publication date: 10 December 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09397

zbMATH Keywords

cubic nonlinear Schrödinger equationpositive single-lobe states

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations in context of PDEs (35B32) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

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Cites Work

• Unnamed Item
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• Threshold phenomena and existence results for NLS ground states on metric graphs
• NLS ground states on graphs
• Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs
• Multiple positive bound states for the subcritical NLS equation on metric graphs
• Standing waves of the quintic NLS equation on the tadpole graph
• Algebraic and analytical tools for the study of the period function
• On the wave length of smooth periodic traveling waves of the Camassa-Holm equation
• Quantum waveguides
• Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
• Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph
• Nonlinear Schrödinger equation on graphs: recent results and open problems
• Surgery principles for the spectral analysis of quantum graphs
• Spectral stability of shifted states on star graphs