Rescaling Symmetry Flow of the Kadomtsev--Petviashvili Hierarchy

We present a new symmetry flow of the Kadomtsev--Petviashvili (KP) hierarchy, which origins from the rescaling of whole "multi-time" valuables. This flow describes the deformation of solutions of the KP hierarchy with respect to a noncommutative parameter. It is shown that the introduced rescaling symmetry flow does not commute with the ordinary evolution flows of the KP hierarchy, but commutes with the evolution flows with respect to slow-variables.