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VOLUME 83 (2006) | ISSUE 10 | PAGE 534
The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation
PACS: 02.30.Ik
Abstract
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.