Standing waves on quantum graphs. (English) Zbl 1507.81100
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.
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
quantum graphs; nonlinear Schrödinger equation; standing waves; variational technique; period function; Dirichlet-to-Neumann mappings; Morse indexSoftware:
QGLABReferences:
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