Certain methods for construction of asymptotics for the Hill equations
On the basis of a method considered by A. Nayfeh we find an asymptotic solution of a special form for the Hill equation in a neighborhood of transition curves. Then, by the averaging method and by means of the corrections obtained up to fourth order we study the same differential equation. We show t...
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| Дата: | 1992 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1992
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7807 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512768324534272 |
|---|---|
| author | Shishanin, O. E. Шишанин, О. Е. |
| author_facet | Shishanin, O. E. Шишанин, О. Е. |
| author_sort | Shishanin, O. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-09-14T12:03:56Z |
| description | On the basis of a method considered by A. Nayfeh we find an asymptotic solution of a special form for the Hill equation in a neighborhood of transition curves. Then, by the averaging method and by means of the corrections obtained up to fourth order we study the same differential equation. We show that the second method also leads to the asymptotics obtained. |
| first_indexed | 2026-03-24T03:34:02Z |
| format | Article |
| fulltext |
Y,UK 517.9
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142 ISSN 0041-6053. Ytcp. MaT. :NCypH., 1992. T. 44, M I
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ISSN 0041 -6053. YKp. ~1ar. [J/CypH., 1992, T. 44, M I 143
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(10)
(11)
ISSN 0041-6053. YKP. Mar. ~ypH., 1992, T . .f4, M I
0134
0135
0136
|
| id | umjimathkievua-article-7807 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:34:02Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1b/ebde3e43d74962dc3ca8ac790fefc61b.pdf |
| spelling | umjimathkievua-article-78072023-09-14T12:03:56Z Certain methods for construction of asymptotics for the Hill equations Некоторые способы построения асимптотик для уравнения Хилла Shishanin, O. E. Шишанин, О. Е. On the basis of a method considered by A. Nayfeh we find an asymptotic solution of a special form for the Hill equation in a neighborhood of transition curves. Then, by the averaging method and by means of the corrections obtained up to fourth order we study the same differential equation. We show that the second method also leads to the asymptotics obtained. На основании метода, рассмотренного А. Найфэ, найдено асимптотическое решение частного вида уравнения Хилла в окрестности переходных кривых. Затем методом усреднения с помощью полученных поправок до четвертого порядка исследуется то же дифференциальное уравнение. Показано, что и второй способ приводит к найденной асимптотике. За допомогою методу, розглянутого А. Найфе, знайдено асимптотичний розв’язок окремого рівняння Хілла в околі перехідних кривих. Потім методом усереднення за допомогою одержаних поправок до четвертого порядку досліджується те ж диференціальне рівняння. Показано, що і другий спосіб приводить до знайденої асимптотики. Institute of Mathematics, NAS of Ukraine 1992-02-04 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7807 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 1 (1992); 142-145 Український математичний журнал; Том 44 № 1 (1992); 142-145 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7807/9474 Copyright (c) 1992 O. E. Shishanin |
| spellingShingle | Shishanin, O. E. Шишанин, О. Е. Certain methods for construction of asymptotics for the Hill equations |
| title | Certain methods for construction of asymptotics for the Hill equations |
| title_alt | Некоторые способы построения асимптотик для уравнения Хилла |
| title_full | Certain methods for construction of asymptotics for the Hill equations |
| title_fullStr | Certain methods for construction of asymptotics for the Hill equations |
| title_full_unstemmed | Certain methods for construction of asymptotics for the Hill equations |
| title_short | Certain methods for construction of asymptotics for the Hill equations |
| title_sort | certain methods for construction of asymptotics for the hill equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7807 |
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