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

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  • We present explicit formal solutions to the systems of equations in two independent variables $t_m$, $x$, $m =1,2,\dots$, 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.
    Mathematics Subject Classification: Primary: 37K10, 37K30; Secondary: 17B80, 22E67.


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