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Exact meromorphic solutions of Schwarzian differential equations

Complex Variables 2021-03-03 v1

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.

Keywords

Cite

@article{arxiv.2103.01393,
  title  = {Exact meromorphic solutions of Schwarzian differential equations},
  author = {Liangwen Liao and Chengfa Wu},
  journal= {arXiv preprint arXiv:2103.01393},
  year   = {2021}
}