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Analytical continuation of two-dimensional wave fieldsстатья
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: 9 апреля 2021 г.
- Авторы: Assier R.C., Shanin A.V.
- Журнал: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Том: 477
- Год издания: 2021
- Издательство: Royal Society of London
- Местоположение издательства: United Kingdom
- Номер статьи: 20200681
- DOI: 10.1098/rspa.2020.0681
- Аннотация: Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffractionproblems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffraction by a half-line or a segment. In the present work, it is shown that such wave fields admit an analytical continuationinto the domain of two complex coordinates. The branch sets of such continuation are given and studied in detail. For a generic scattering problem, it is shown that the set of all branches of the multi-valued analytical continuation of the field has a finite basis.Each basis function is expressed explicitly as a Green’s integral along so-called double-eight contours. The finite basis property is important in the context of coordinate equations, introduced and used by theauthors previously, as illustrated in this article for the particular case of diffraction by a segment.
- Добавил в систему: Шанин Андрей Владимирович
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