|
Modelirovanie i Analiz Informatsionnykh Sistem, 2014, Volume 21, Number 5, Pages 49–60
(Mi mais398)
|
|
|
|
Doubly periodic meromorphic solutions of autonomous nonlinear differential equations
M. V. Demina, N. A. Kudryashov National Engineering Physics Institute "MEPhI", Moscow
Abstract:
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.
Keywords:
meromorphic solutions, elliptic solutions, autonomous nonlinear differential equations.
Received: 12.08.2014
Citation:
M. V. Demina, N. A. Kudryashov, “Doubly periodic meromorphic solutions of autonomous nonlinear differential equations”, Model. Anal. Inform. Sist., 21:5 (2014), 49–60
Linking options:
https://www.mathnet.ru/eng/mais398 https://www.mathnet.ru/eng/mais/v21/i5/p49
|
Statistics & downloads: |
Abstract page: | 314 | Full-text PDF : | 212 | References: | 50 |
|