Weak Lax pair formulation for a new integrable nonlinear equation in 2+1 dimensions

Abstract

A new integrable nonlinear equation is derived from a previously known integrable equation by means of an asymptotically exact nonlinear reduction method based on Fourier expansion and spatio-temporal rescaling. The new equation is likely to be of applicative relevance due to the particular features of the reduction method. The integrability by the weak Lax pair formulation and the inverse scattering method is explicitly demonstrated, by applying the reduction technique to the Lax pair of the starting equation, and the corresponding Lax pair of the new equation is found.