Explicit Meromorphic Solutions of a Second Order Briot–Bouquet Differential Equation

In this paper, a special second-order Briot–Bouquet differential equation is studied. We construct explicit meromorphic solutions by the Kowalevski–Gambier method and a careful discussion. How we take into account the corresponding series at zeros, as opposed to the Laurent series at poles. This met...

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Bibliographic Details
Published in:Computational methods and function theory 2024-12, Vol.24 (4), p.725-746
Main Authors: Shi, Xujie, Zhang, Jie, Liao, Liangwen
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
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Summary:In this paper, a special second-order Briot–Bouquet differential equation is studied. We construct explicit meromorphic solutions by the Kowalevski–Gambier method and a careful discussion. How we take into account the corresponding series at zeros, as opposed to the Laurent series at poles. This method is also useful for the study of many other non-linear differential equations.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-023-00519-y