THE KADOMTSEV-PETVIASHVILI EQUATION AS A SOURCE OF INTEGRABLE MODEL-EQUATIONS

A new integrable and nonlinear partial differential equation (PDE) in 2 + 1 dimensions is obtained, by an asymptotically exact reduction met hod based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev-Petviashvili equation. The integrability property is explici tly demonstrated, by exhibiting the corresponding Lax pair, that is ob tained by applying the reduction technique to the Lax pair of the Kado mtsev-Petviashvili equation. This model equation is likely to be of ap plicative relevance, because it may be considered a consistent approxi mation of a large class of nonlinear evolution PDEs. (C) 1996 American Institute of Physics.