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Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series

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Abstract

A package facilitating search for analytic solutions of nonintegrable systems of autonomous ordinary differential equations is suggested. The algorithm discussed, which is a generalization of the Conte-Musette method, allows one to obtain single-valued and multivalued analytical solutions that were known to exist only in the form of formal Laurent and Puiseux series (obtained, for example, by means of the Painlevé analysis), respectively. Solutions in the form of the formal Laurent series and procedures from the package discussed are used not only for constructing elliptic solutions but also for proving impossibility of such construction. The suggested procedures have been implemented as packages in Maple and REDUCE.

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  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Vorob’evy gory, Moscow, 119992, Russia

    S. Yu. Vernov

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Original Russian Text © S.Yu. Vernov, 2006, published in Programmirovanie, 2006, Vol. 32, No. 2.

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Vernov, S.Y. Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series. Program Comput Soft 32, 77–83 (2006). https://doi.org/10.1134/S0361768806020046

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  • DOI: https://doi.org/10.1134/S0361768806020046

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