Standing waves on quantum graphs

Abstract

We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational theory, dynamical systems on a phase plane, and the Dirichlet-to-Neumann mappings.

arXiv comment48 pages; 19 figures

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Cited by in corpus (3)

• Normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities
• Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
• Ground states for the NLS on non-compact graphs with an attractive potential