The Schrödinger equation on a star-shaped graph under general coupling conditions

DOI10.1088/1751-8121/aaf3fczbMath1422.81098arXiv1711.10235OpenAlexW2950372721MaRDI QIDQ5235201

Liviu I. Ignat, Andreea Grecu

Publication date: 7 October 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10235

zbMATH Keywords

Schrödinger operatordispersionquantum graphsStrichartz estimatesnon- linear Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Distance in graphs (05C12) Dispersion theory, dispersion relations arising in quantum theory (81U30) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (7)

Standing waves on quantum graphs ⋮ On the nonlinear Dirac equation on noncompact metric graphs ⋮ Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph ⋮ \(L^p-L^{p'}\) estimates for matrix Schrödinger equations ⋮ Exponential stability for the nonlinear Schrödinger equation on a star-shaped network ⋮ Nonlinear dispersive equations: classical and new frameworks ⋮ Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition

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