Abstract
The Kadomtsev-Petviashvili (KP) hierarchy has infinitely many Hamiltonian pairs, then th pair of them is associated withL n, whereL is the pseudodifferential operator (PDO) [3,4]. In this paper, by the factorizationL n=L n ...L 1 withL j ,j=1,...,n being the independent PDOs, we construct the Miura transformation for the KP, which leads to a decomposition of the second Hamiltonian structure in then th pair to a direct sum. Each term in the sum is the second structure in the initial pair associated withL j . When we impose a constraint (1.9) (i.e a new type of reduction) to the KP hierarchy, we obtain the similar results for the constrained KP hierarchy. In particular the second Hamiltonian structure for this hierarchy is transformed to a vastly simpler one.
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Cheng, Y. Modifying the KP, then th constrained KP hierarchies and their Hamiltonian structures. Commun.Math. Phys. 171, 661–682 (1995). https://doi.org/10.1007/BF02104682
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DOI: https://doi.org/10.1007/BF02104682