Scattering of radiation by a quasiperiodic two-dimensional medium. (English) Zbl 0642.35049
We study the scattering of radiation by a medium presenting inhomogeneities distributed in a quasiperiodic way. We show the existence of quasiperiodic solutions of the two-dimensional stationary wave equation, under certain conditions on the index of refraction, using a technique based on Dinaburg-Sinai method for one-dimensional Schrödinger equation with a quasiperiodic potential. Moreover we show that the energy spectrum contains a nonempty absolutely continuous component, with a subset having high degeneracy, provided the inhomogeneities are small enough.
MSC:
| 35L05 | Wave equation |
| 78A45 | Diffraction, scattering |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35B10 | Periodic solutions to PDEs |
| 35P05 | General topics in linear spectral theory for PDEs |
Keywords:
absolutely continuous spectrum; degeneracy; scattering of radiation; quasiperiodic; existence; stationary wave equation; index of refraction; Dinaburg-Sinai method; Schrödinger equation; quasiperiodic potential; energy spectrumReferences:
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