The KW theorem for the SKP hierarchy

The supersymmetric Kadomtsev-Petviashvili (SKP) hierarchy is first introduced by Manin and Radul. In this letter, by the factorization Ln=LnLn−1⋯L1 with Lj=D+uj,0+uj,−1D−1+uj,−2D−2+⋯, j=1,2⋯n, being the independent super-pseudodifferential operators (SΨDOs), we construct the supersymmetric Miura transformation for the SKP hierarchy, which leads to decomposition of the second Poisson brackets based on Ln to a direct sum. Each term in the sum contains the second brackets for Lj.