The Cauchy Problem on the Plane for the Dispersionless Kadomtsev–Petviashvili Equation

We construct the formal solution of the Cauchy problem for the dispersionless Kadomtsev–Petviashvili equation as application of the Inverse Scattering Transform for the vector field corresponding to a Newtonian particle in a time-dependent potential. This is in full analogy with the Cauchy problem for the Kadomtsev–Petviashvili equation, associated with the Inverse Scattering Transform of the time dependent Schrödinger operator for a quantum particle in a time-dependent potential.