Coupled Painlevé III systems with affine Weyl group symmetry of types B₅⁽¹⁾,D₅⁽¹⁾ and D₆⁽²⁾

2007/04/19 by Sasano, Yusuke
#34M45 #34M55 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0704.2467

Abstract

We find and study four kinds of five-parameter family of six-dimensional coupled Painlevé III systems with affine Weyl group symmetry of types D₅⁽¹⁾,B₅⁽¹⁾ and D₆⁽²⁾. We show that each system is equivalent by an explicit birational and symplectic transformation, respectively. We also show that we characterize each system from the viewpoint of holomorphy.

Related

• Coupled Painlevé III systems with affine Weyl group symmetry of types B₄⁽¹⁾, D₄⁽¹⁾ and D₅⁽²⁾
• Coupled Painlevé III system with affine Weyl group symmetry of type D₆⁽¹⁾
• Coupled Painlevé systems with affine Weyl group symmetry of types D₃⁽²⁾ and D₅⁽²⁾
• Coupled Painlevé systems with affine Weyl group symmetry of types A₇⁽²⁾,A₅⁽²⁾ and D₄⁽³⁾
• Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type E₆⁽²⁾