Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations
The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find an elliptic solution of an autonomous nonlinear ordinary differential equation is described. The method does not require integrating additional diff...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-10-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/84 |
| _version_ | 1797877908184760320 |
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| author | M. V. Demina N. A. Kudryashov |
| author_facet | M. V. Demina N. A. Kudryashov |
| author_sort | M. V. Demina |
| collection | DOAJ |
| description | The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find an elliptic solution of an autonomous nonlinear ordinary differential equation is described. The method does not require integrating additional differential equations. Much attention is paid to the case of elliptic solutions with several poles inside a parallelogram of periods. With the help of the method we find elliptic solutions up to the fourth order inclusively of an ordinary differential equation with a number of physical applications. The method admits a natural generalization and can be used to find elliptic solutions satisfying systems of ordinary differential equations. |
| first_indexed | 2024-04-10T02:25:25Z |
| format | Article |
| id | doaj.art-daee13f11f734072a3098d5f0040e9d9 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:25:25Z |
| publishDate | 2014-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-daee13f11f734072a3098d5f0040e9d92023-03-13T08:07:32ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-10-01215496010.18255/1818-1015-2014-5-49-6078Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential EquationsM. V. Demina0N. A. Kudryashov1Национальный Исследовательский Ядерный Университет «МИФИ»Национальный Исследовательский Ядерный Университет «МИФИ»The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find an elliptic solution of an autonomous nonlinear ordinary differential equation is described. The method does not require integrating additional differential equations. Much attention is paid to the case of elliptic solutions with several poles inside a parallelogram of periods. With the help of the method we find elliptic solutions up to the fourth order inclusively of an ordinary differential equation with a number of physical applications. The method admits a natural generalization and can be used to find elliptic solutions satisfying systems of ordinary differential equations.https://www.mais-journal.ru/jour/article/view/84мероморфные решенияэллиптические решенияавтономные нелинейные дифференциальные уравнения |
| spellingShingle | M. V. Demina N. A. Kudryashov Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations Моделирование и анализ информационных систем мероморфные решения эллиптические решения автономные нелинейные дифференциальные уравнения |
| title | Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations |
| title_full | Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations |
| title_fullStr | Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations |
| title_full_unstemmed | Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations |
| title_short | Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations |
| title_sort | doubly periodic meromorphic solutions of autonomous nonlinear differential equations |
| topic | мероморфные решения эллиптические решения автономные нелинейные дифференциальные уравнения |
| url | https://www.mais-journal.ru/jour/article/view/84 |
| work_keys_str_mv | AT mvdemina doublyperiodicmeromorphicsolutionsofautonomousnonlineardifferentialequations AT nakudryashov doublyperiodicmeromorphicsolutionsofautonomousnonlineardifferentialequations |