Non-Integrability of the Sasano System of Type $D_5^{(1)}$ and Stokes Phenomena
Year: 2025
Type: article
Abstract: In 2006, Y. Sasano proposed higher-order Painleve systems, which admit affine Weyl group symmetry of type $D^{(1)}_l$, $l=4, 5, 6, \dots$. In this paper, we study the integrability of a four-dimensional Painlevé system, which has symmetry under the extended affine Weyl group $\widetilde{W}\bigl(D^{(1)}_5\bigr)$ and which we call the Sasano system of type $D^{(1)}_5$. We prove that one family of the Sasano system of type $D^{(1)}_5$ is not integrable by rational first integrals. We describe Stokes phenomena relative to a subsystem of the second normal variational equations. This approach allows us to compute in an explicit way the corresponding differential Galois group and therefore to determine whether the connected component of its unit element is not Abelian. Applying the Morales-Ramis-Simo theory, we establish a non-integrable result.
Author: Tsvetana Stoyanova
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408913416