Kadomtsev-Petviashvili hierarchies beyond standard settings

Abstract We present a general framework for Kadomtsev–Petviashvili (KP) hierarchies beyond standard settings, relying on algebraic and geometric extensions of the classical theory including diffeological algebras, non-commutative structures, and generalized derivations. Our approach encompasses both formal and non-formal operator settings and leads to a general criterion for the integrability and well-posedness of KP-like equations.