Explicit Meromorphic Solutions of a Certain Briot-Bouquet Differential Equations


Xujie SHI,Liangwen LIAO,Song ZHANG.Explicit Meromorphic Solutions of a Certain Briot-Bouquet Differential Equations[J].Chinese Annals of Mathematics B,2020,41(3):383~396
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Xujie SHI; Liangwen LIAO;Song ZHANG


This work was supported by the National Natural Science Foundation of China (No.11671191).
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.


Movable poles, Differential equations, Meromorphic solutions


30D35, 33E30, 30D30
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