The KW theorem for the SKP hierarchy. (English) Zbl 0966.37033

Summary: The supersymmetric Kadomtsev-Petviashvili (SKP) hierarchy was first introduced by Yu. I. Manin and A. O. Radul [Commun. Math. Phys. 98, 65-77 (1985; Zbl 0607.35075)]. In this letter, by the factorization \(L^n=L_nL_{n-1}\cdots L_1\) with \(L_j=D+u_{j,0}+u_{j,-1}D^{-1}+u_{j,-2}D^{-2}+\cdots\), \(j=1,2\cdots n\), being the independent super-pseudodifferential operators, we construct the supersymmetric Miura transformation for the SKP hierarchy, which leads to decomposition of the second Poisson brackets based on \(L^n\) to a direct sum. Each term in the sum contains the second brackets for \(L_j\).


37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q58 Other completely integrable PDE (MSC2000)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems


Zbl 0607.35075
Full Text: DOI


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