The Dbar-dressing method for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Abstract

Abstract In this work, the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation is studied by means of the ∂ ¯ -dressing method. A new ∂ ¯ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation. Based on solving the ∂ ¯ equation and choosing the proper spectral transformation, the solution of the DJKM equation is constructed. Furthermore, the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.