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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.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups