Affine Weyl group symmetries of Frobenius Painlevé equations. (13th December 2019)

• Record Type: Journal Article
• Authors: Wang, Haifeng; Li, Chuanzhong
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 6(2020)
• Page Start: 3238
• Page End: 3252
• Publication Date: 2019-12-13
• Subjects: affine Weyl group symmetry -- Frobenius Painlevé II equation -- Frobenius Painlevé IV equation -- Hamilton system -- similarity reduction; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6116
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we introduce a Frobenius Painlevé IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painlevé IV equation. Then, we construct the Lax pair of the Frobenius Painlevé IV equation. Furthermore, we recall the Frobenius modified KP hierarchy and the Frobenius KP hierarchy by bilinear equations, then we show how to get Frobenius Painlevé IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painlevé IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painlevé II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painlevé II equation.