Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations
https://doi.org/10.18255/1818-1015-2014-5-49-60
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.
About the Authors
M. V. Demina
National Research Nuclear University MEPhI
Russian Federation
доктор физико-математических наук, профессор, заведующий кафедрой прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia
Russian Federation
доктор физико-математических наук, профессор, заведующий кафедрой прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia
N. A. Kudryashov
National Research Nuclear University MEPhI
Russian Federation
кандидат физико-математических наук, доцент кафедры прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia
Russian Federation
кандидат физико-математических наук, доцент кафедры прикладной математики; Kashirskoe shosse, 31, Moscow, 115409, Russia
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Review
For citations:
Demina M.V., Kudryashov N.A. Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations. Modeling and Analysis of Information Systems. 2014;21(5):49-60. (In Russ.) https://doi.org/10.18255/1818-1015-2014-5-49-60
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