Affine Weyl group symmetries of Frobenius Painleve equations

摘要

In this paper, we introduce a Frobenius Painleve IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painleve IV equation. Then, we construct the Lax pair of the Frobenius Painleve 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 Painleve IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painleve IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painleve II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painleve II equation.