Backlund transformation of Frobenius Painleve equations

In this paper, in order to generalize the Painleve equations, we give a Z(n)-Painleve IV equation which can apply Backlund transformations to explore. And these Backlund transformations can generate new solutions from seed solutions. Similarly, we also introduce a Frobenius Painleve I equation and Frobenius Painleve III equation. Then, we find the connection between the Frobenius KP hierarchy and Frobenius Painleve I equation by the Virasoro constraint. Further, in order to seek different aspects of Painleve equations, we introduce the Lax pair, Hirota bilinear equation and tau functions. Moreover, some Frobenius Okamoto-like equations and Frobenius Toda-like equations can also help us to explore these equations.