Abstract
We show that the N = 1 supersymmetric Kadomtsev-Petviashvili (SKP) equation of Manin and Radul can be embedded into recently formulated N = 1 self-dual supersymmetric Yang-Mills theories after appropriate dimensional reduction and truncation, which yield three-dimensional supersymmetric Chern-Simons theories. Based on this result, we also give a conjectural N = 2 SKP equation. Subsequently some exact solutions of these systems including fermionic fields are given.
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