Explicit Meromorphic Solutions of a Certain Briot-Bouquet Differential Equations

Xujie Shi; Liangwen Liao; Song Zhang

doi:10.1007/s11401-020-0205-x

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (3) : 383 -396. DOI: 10.1007/s11401-020-0205-x

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Explicit Meromorphic Solutions of a Certain Briot-Bouquet Differential Equations

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Abstract

This paper deals with the Briot-Bouquet differential equations with degree three. The previous result shows that all the meromorphic solutions belong to W. Here, by applying the Kowalevski-Gambier method, the authors give all the possible explicit meromorphic solutions. The result is more applicable. Also, this method can be used to deal with the more general Briot-Bouquet differential equations.

Keywords

Movable poles / Differential equations / Meromorphic solutions

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Xujie Shi, Liangwen Liao, Song Zhang. Explicit Meromorphic Solutions of a Certain Briot-Bouquet Differential Equations. Chinese Annals of Mathematics, Series B, 2020, 41(3): 383-396 DOI:10.1007/s11401-020-0205-x

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