Exact meromorphic solutions of Schwarzian differential equations

Liangwen Liao; Chengfa Wu

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arXiv · 2103.01393

Exact meromorphic solutions of Schwarzian differential equations

Liangwen Liao·Chengfa Wu

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Abstract

This paper studies exact meromorphic solutions of the autonomous Schwarzian differential equations. All transcendental meromorphic solutions of five canonical types (among six) of the autonomous Schwarzian differential equations are constructed explicitly. In particular, the solutions of four types are shown to be elliptic functions. Also, all transcendental meromorphic solutions that are locally injective or possess a Picard exceptional value are characterized for the remaining canonical type.

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Liangwen Liao, Chengfa Wu. 2021-03-02. Exact meromorphic solutions of Schwarzian differential equations. https://arxiv.org/abs/2103.01393

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