The Kadomtsev-Petviashvili Hierarchy and the Mulase Factorization of Formal Lie Groups

We present explicit formal solutions to the systems of equations in two independent variables tm, x, m = 1, 2,., of the Kadomtsev- Petviashvili hierarchy. The main tools used are a Birkhoff-like factorization of formal Lie groups due to M. Mulase, and the classical theory of A.G. Reyman and M.A. Semenov-Tian-Shansky on the integration of Hamiltonian systems on coadjoint orbits using r-matrices. Our paper also contains full proofs of Mulase s results. © American Institute of Mathematical Sciences.