A 3 × 3 Lax Form for the -Painlevé Equation of Type ₆

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Author: Park, Kanam
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212037
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A 3 × 3 Lax Form for the -Painlevé Equation of Type ₆. Kanam Park. SIGMA 19 (2023), 094, 17 pages

For the -Painlevé equation with affine Weyl group symmetry of type ⁽¹⁾₆, a 2 × 2 matrix Lax form and a second-order scalar lax form were known. We give a new 3 × 3 matrix Lax form and a third order scalar equation related to it. Continuous limit is also discussed.