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

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

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S. V. Manakov, P. M. Santini. 2006-04-11. The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation. https://doi.org/10.1134/s0021364006100080

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