Standing waves on quantum graphs

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-N...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-06, Vol.55 (24), p.243001
Main Authors: Kairzhan, Adilbek, Noja, Diego, Pelinovsky, Dmitry E
Format: Article
Language:English
Subjects:
Dirichlet-to-Neumann mappings
Morse index
nonlinear Schrödinger equation
period function
quantum graphs
standing waves
variational technique
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Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac6c60