Meromorphic solutions to the q-Painlevé equations around the origin

30th International Colloquium on Group Theoretical Methods in Physics

Ohyama, Y.^1

Department of Mathematics, Osaka University, 1-1 Machikaneyama-machi, Toyonaka

560-0043, Japan^1

关键词: Generic parameters;    Linear connections;    Meromorphic solutions;    Painleve equations;    Singular points;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012063/pdf
DOI  :  10.1088/1742-6596/597/1/012063

来源: IOP

【 摘 要 】

We study meromorphic solutions to the q-Painleve equations with type VI, V, III around the origin. Since the origin of q-PVI, q-PVand q-PIIIare singular points of the q-Briot- Bouquet type, they have holomorphic solutions for generic parameters. The q-PVI, q-PVand q-PIIIhave four, three and two meromorphic solutions around the origin respectively. We can solve linear connection problems for holomorphic solutions.