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

Details The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation

2006-04-11

arxiv.org/abs/nlin/0604023v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, submitted to JETP Letters

Scientific paper

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.

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