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}
}