Symmetries in the system of type D₄⁽¹⁾

2007/04/18 by Yusuke Sasano, Sasano, Yusuke · 2 citations
Mathematics · Physics and Astronomy · #32S65 #34M45 #34M55 #58F05 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:32S65 #msc:34M45 #msc:34M55 #msc:58F05

paper · pdf · doi:10.48550/arxiv.0704.2331

4 pages, 1 figure

arxiv created 2007/04/18 · openalex publication_date 2007/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a 4-parameter family of coupled Painlevé III systems in dimension four with affine Weyl group symmetry of type D₄⁽¹⁾. We also propose its symmetric form in which the D₄⁽¹⁾-symmetries become clearly visible.

Cited by

• Coupled Painlevé systems in dimension four with affine Weyl group symmetry of types A₄⁽²⁾ and A₁⁽¹⁾
• Ordinary differential systems in dimension three with affine Weyl group symmetry of types D₄⁽¹⁾,B₃⁽¹⁾,G₂⁽¹⁾,D₃⁽²⁾ and A₂⁽²⁾

Related

• Symmetries in the system of type A₅⁽²⁾
• Coupled Painlevé III systems with affine Weyl group symmetry of types B₄⁽¹⁾, D₄⁽¹⁾ and D₅⁽²⁾
• Four-dimensional Painlevé systems of types D₅⁽¹⁾ and B₄⁽¹⁾
• Coupled Painlevé III system with affine Weyl group symmetry of type D₆⁽¹⁾
• Coupled Painlevé systems in dimension four with affine Weyl group symmetry of types A₄⁽²⁾ and A₁⁽¹⁾