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.
Kairzhan, A., Noja, D., Pelinovsky, D. (2022). Standing waves on quantum graphs. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 55(24) [10.1088/1751-8121/ac6c60].
Standing waves on quantum graphs
Noja D.;
2022
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.
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