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Алгебра и анализ, 2021, том 33, выпуск 2, страницы 275–297
(Mi aa1755)
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Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
Статьи
Searchlight asymptotics for high-frequency scattering by boundary inflection
V. P. Smyshlyaev, I. V. Kamotski Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
Аннотация:
The paper is devoted to an inner problem for a whispering gallery high-frequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schrödinger equation on a half-line with a potential linear in both space and time appears fundamental for describing transitions from modal to scattered asymptotic patterns, and despite having been intensively studied over several decades remains largely unsolved. The solution past the inflection point is shown to have a “searchlight” asymptotics corresponding to a beam concentrated near the limit ray. Certain decay and smoothness properties of the related searchlight amplitude are established. Further interpretations of the above result are also discussed: the existence of the associated generalised wave operator, and of a version of a unitary scattering operator connecting the modal and scattered asymptotic regimes.
Ключевые слова:
diffraction, whispering gallery, boundary inflection, wave operator.
Поступила в редакцию: 05.11.2020
Образец цитирования:
V. P. Smyshlyaev, I. V. Kamotski, “Searchlight asymptotics for high-frequency scattering by boundary inflection”, Алгебра и анализ, 33:2 (2021), 275–297; St. Petersburg Math. J., 33:2 (2022), 387–403
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1755 https://www.mathnet.ru/rus/aa/v33/i2/p275
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Страница аннотации: | 142 | PDF полного текста: | 34 | Список литературы: | 19 | Первая страница: | 15 |
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