Coupled Painlevé systems with affine Weyl group symmetry of types D₃⁽²⁾ and D₅⁽²⁾

2007/05/31 by Yusuke Sasano, Sasano, Yusuke
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.0705.4540

Abstract

In this paper, we find a two-parameter family of coupled Painlevé systems in dimension four with affine Weyl group symmetry of type D₃⁽²⁾. We also find a four-parameter family of 2-coupled D₃⁽²⁾-systems in dimension eight with affine Weyl group symmetry of type D₅⁽²⁾. We show that for each system, we give its symmetry and holomorphy conditions, respectively. These symmetries, holomorphy conditions and invariant divisors are new.

Citations

• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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