The ∂̄-dressing method for the (2+1)-dimensional Jimbo-Miwa equation

Abstract

The (2+1)-dimensional Jimbo-Miwa equation is analyzed by means of the ∂ ¯ \bar {{\partial }} -dressing method. By means of the characteristic function and Green’s function of the Lax representation, the problem has been transformed into a new ∂ ¯ \bar {{\partial }} problem. A solution is constructed based on solving the ∂ ¯ \bar {{\partial }} problem with the help of Cauchy-Green formula and choosing the proper spectral transformation. Furthermore, we can obtain the solution formally of the Jimbo-Miwa equation when the time evolution of the spectral data is determined.