A generalized Hirota equation in 2+1 dimensions

Abstract

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.