Scattering anomalies in a resonator above the thresholds of the continuous spectrum

S.A. Nazarov

Результат исследований: Научные публикации в периодических изданияхстатья

8 Цитирования (Scopus)

Аннотация

© 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.We consider the Dirichlet spectral problem for the Laplace operator in a multi-dimensional domain with a cylindrical outlet to infinity, a Helmholtz resonator. Using asymptotic analysis of the scattering matrix we demonstrate different types of reflection of high-amplitude near-threshold waves. One scattering type or another, unstable or stable with respect to variations of the resonator shapes, is determined by the presence or absence of stabilizing solutions at the threshold frequency, respectively. In a waveguide with two cylindrical outlets to infinity, we discover the effect of almost complete passage of the wave under 'fine tuning' of the resonator.
Язык оригиналаанглийский
Страницы (с-по)782-813
ЖурналSbornik Mathematics
Номер выпуска6
DOI
СостояниеОпубликовано - 2015

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