Supersymmetric structure of Kadomtsev–Petviashvili equation: Connection between supersymmetry and Bäcklund transformations

Factorization of the Sato integrodifferential operator that gives the hierarchy of the Kadomtsev–Petviashvili equation is considered. The supersymmetric structure of this hierarchy is investigated by means of the factorization. A connection between the Miura transformations, Bäcklund transformations, and supersymmetry is established.