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 Schroedinger operator for a quantum particle in a time-dependent potential. 
S. V. Manakov and P. M. Santini