|
ИСТИНА |
Войти в систему Регистрация |
ФНКЦ РР |
||
Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifoldsстатья
Статья опубликована в журнале из списка RSCI Web of Science
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 17 января 2018 г.
- Авторы: Dobrokhotov S.Yu, Nazaikinskii V.E.
- Журнал: Russian Journal of Mathematical Physics
- Том: 24
- Номер: 1
- Год издания: 2017
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 127
- Последняя страница: 133
- DOI: 10.1134/S1061920817010113
- Аннотация: The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
- Добавил в систему: Левитин Александр Леонидович