Geodesic
Doubly periodic meromorphic solutions of autonomous nonlinear differential equations
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 49-60

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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.
Mots-clés : meromorphic solutions, elliptic solutions
Keywords: autonomous nonlinear differential equations. 
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     author = {M. V. Demina and N. A. Kudryashov},
     title = {Doubly periodic meromorphic solutions of autonomous nonlinear differential equations},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {49--60},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a2/}
}
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M. V. Demina; N. A. Kudryashov. Doubly periodic meromorphic solutions of autonomous nonlinear differential equations. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 5, pp. 49-60. http://geodesic.mathdoc.fr/item/MAIS_2014_21_5_a2/