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Affine Weyl group symmetries of Frobenius Painlevé equations
Author(s) -
Wang Haifeng,
Li Chuanzhong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6116
Subject(s) - mathematics , frobenius group , weyl group , pure mathematics , frobenius theorem (differential topology) , frobenius solution to the hypergeometric equation , affine transformation , frobenius algebra , homogeneous space , hierarchy , algebra over a field , hypergeometric function , geometry , generalized hypergeometric function , algebra representation , scalar curvature , curvature , ricci flat manifold , economics , market economy , hypergeometric function of a matrix argument
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.