Cauchy problem on the plane for the dispersionless Kadomtsev-Petviashvili equation

@article{Manakov2006CauchyPO,
  title={Cauchy problem on the plane for the dispersionless Kadomtsev-Petviashvili equation},
  author={S. Manakov and P M Santini},
  journal={JETP Letters},
  year={2006},
  volume={83},
  pages={462-466}
}
We construct the formal solution to the Cauchy problem for the dispersionless Kadomtsev-Petviashvili equation as an 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. 
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