On the continuum limit for a model of binary waveguide arrays. (English) Zbl 1512.35501
Author’s abstract: In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal arguments and numerical simulations present in the Physics literature.
Reviewer: Abderrazek Benhassine (Monastir)
MSC:
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35Q40 | PDEs in connection with quantum mechanics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 81Q37 | Quantum dots, waveguides, ratchets, etc. |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
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