Standing waves on quantum graphs
Adilbek Kairzhan, Diego Noja, Dmitry E. Pelinovsky
Abstract
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.
Topics & Concepts
Quantum graphQuantumMathematicsNonlinear systemDirichlet distributionPartial differential equationStability (learning theory)Mathematical analysisPhysicsQuantum mechanicsComputer scienceBoundary value problemMachine learningAdvanced Mathematical Physics ProblemsSpectral Theory in Mathematical PhysicsNonlinear Photonic Systems