$$\bar{\partial }$$-Dressing Method for a Generalized (2 + 1)-Dimensional Nonlinear Wave Equation

Abstract The main purpose of this work is solving a generalized (2 + 1)-dimensional nonlinear wave equation via $$\bar{\partial }$$ ∂ ¯ -dressing method. key to process establish connection between characteristic functions and -problem. With use Fourier transformation inverse transformation, we obtain explicit expressions Green’s function give two corresponding general potential. Further, the -problem constructed by calculating derivative function. solution can be shown Cauchy–Green formula, after determining time evolution scatter data, solutions equation.