A Kadomtsev–Petviashvili Hierarchy Driven by Equation Manifolds

The fact that (formally integrable) differential equations determine sub-bundles of appropriate infinite jet bundles allows us to introduce a ‘‘driven’’ Kadomtsev–Petviashvili (KP) hierarchy. We solve this hierarchy and we observe, as an application, that each solution to the KdV equation determines smooth solutions to our full KP hierarchy, and that these solutions are also smooth with respect to the ‘‘seed’’ (or initial) corresponding KdV solution.