Generalized Hirota equation in 2+1 dimensions

Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, a new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained starting from the Kadomtsev-Petviashvili equation. We apply the reduction technique to the Lax pair of the Kadomtsev-Petviashvili equation and demonstrate the integrability property of the new equation, because we obtain the corresponding Lax pair. The new equation reduces to the Hirota equation in the 1+1-dimensional limit. (C) 1998 American Institute of Physics. [S0022-2488(98)03911-5].