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Doubly periodic meromorphic solutions of autonomous nonlinear differential equations

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Abstract

The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find any elliptic solution of an autonomous nonlinear ordinary differential equation is described. The method does not require integrating additional differential equations. Much attention is being paid to the case of elliptic solutions with several poles in 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.

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Authors and Affiliations

  1. National Research Nuclear University MEPhI, Kashirskoe shosse, 31, Moscow, 115409, Russia

    M. V. Demina & N. A. Kudryashov

Authors
  1. M. V. Demina
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  2. N. A. Kudryashov
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Correspondence to M. V. Demina.

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Demina, M.V., Kudryashov, N.A. Doubly periodic meromorphic solutions of autonomous nonlinear differential equations. Aut. Control Comp. Sci. 48, 633–641 (2014). https://doi.org/10.3103/S0146411614070207

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  • DOI: https://doi.org/10.3103/S0146411614070207

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