THE DIRAC-EQUATION AND INTEGRABLE SYSTEMS OF KP TYPE

The propagator for the 2D heat equation in an arbitrary linear space i s shown to give solutions of the two-component Kadomtsev-Petviashvilii (KP) equations, also called Davey-Stewartson system. This propagator is subject to the Klein-Gordon equation and its right-derivatives are required to be of rank one, that imply that it can be expressed in ter ms of solutions of the Dirac equation. Large families of solutions of the two-component Kadomtsev-Petviashvilii equations are constructed in terms of solutions of the heat and Dirac equations. Particular attent ion is paid to the real reductions of the Davey-Stewartson type, recov ering in this way the line solitons and the multidromion solutions. Mo reover, new solutions to the Davey-Stewartson I are presented as massi ve deformations of the dromion.