Exact meromorphic solutions of Schwarzian differential equations
Exact meromorphic solutions of Schwarzian differential equations
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DOI：
10.1007/s00209-021-02855-y
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发表时间：
2021-03
影响因子：
0.8
通讯作者：
L. Liao;Chengfa Wu
中科院分区：
文献类型：
--
作者：
L. Liao;Chengfa Wu
研究了自治Schwarzian微分方程的精确亚纯解。构造了五种典型类型（其中六种）的自治Schwarzian微分方程的全部超越亚纯解。特别地，四种类型的解被证明是椭圆函数。此外，所有的超越亚纯解是局部内射或具有皮卡德例外值的特征在于其余的典型类型。
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.