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