A novel systematical solution procedure of the (2+1)-dimensional Konopelchenko–Dubrovsky equation is employed on the basis of the $\bar{\partial }$-dressing method. The eigenfunctions and Green’s function of the Lax pair play a fairly important role in constructing the scattering equation. By analyzing the analyticity of the eigenfunctions and Green’s function, a new $\bar{\partial }$ problem is introduced to help explore the solution with the help of Cauchy–Green formula and choosing the proper spectral transformation. Furthermore, we can work out the solution formally of the Konopelchenko–Dubrovsky equation from inverse spectral problem once the time evolution of the spectral data is determined.

(2+1) 维 Konopelchenko-Dubrovsky 方程的一种新的系统求解过程是基于$\bar{\partial }$- 着装方法。Lax 对的特征函数和格林函数在构造散射方程中起着相当重要的作用。通过分析本征函数和格林函数的解析性，提出了一个新的$\bar{\partial }$引入问题以帮助在柯西-格林公式的帮助下探索解决方案并选择适当的光谱变换。此外，一旦确定了光谱数据的时间演化，我们就可以从反光谱问题中正式求解 Konopelchenko-Dubrovsky 方程。