Dbar-dressing method for a new (2+1)-dimensional generalized Kadomtsev–Petviashvili equation

The primary purpose of this work is to consider a $(2+1)$-dimensional generalized KP equation via $\bar{\partial }$-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the $\bar{\partial }$ derivative, a $\bar{\partial }$ problem arises naturally. Based on the symmetry of the Green function, we give a standard $\bar{\partial }$ equation, and its solution is expressed by the Cauchy formula.