Symmetry in the Painlevé systems and their extensions to four-dimensional systems

Abstract

We give a new approach to the symmetries of the Painlevé equations $P_V,P_{IV},P_{III}$ and $P_{II}$, respectively. Moreover, we make natural extensions to fourth-order analogues for each of the Painlevé equations $P_V$ and $P_{III}$, respectively, which are natural in the sense that they preserve the symmetries.

32 pages, 16 figures

References in corpus (2)

• Higher order Painlevé equations of type $A_l^{(1)}$
• An augmentation of the phase space of the system of type A^{(1)}_4

Cited by in corpus (2)

• Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations
• Studies on the second member of the second Painlevé hierarchy