We apply the $\bar{\partial }$-dressing method to study a coupled Gerdjikov–Ivanov (GI) equation. Compared with results on the classical coupled GI equation, more general spatial and a time singular spectral problems associated with GI equation are derived from a local 2 × 2 matrix $\bar{\partial }$-equation via two linear constraint equations. A more general GI hierarchy with source is proposed by using recursive operator. The $N$-solitons of the coupled GI equation are constructed still based the $\bar{\partial }$-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. The results on the GI equation can be recovered from the conclusion given above as special reductions.

我们应用 $\bar{\partial }$耦合Gerdjikov-Ivanov（GI）方程的配比方法。与经典耦合GI方程的结果相比，从局部2×2矩阵导出了与GI方程相关的更一般的空间和时间奇异谱问题$\bar{\partial }$通过两个线性约束方程的方程。通过使用递归运算符，提出了一个更通用的带有源的GI层次结构。的$ñ$耦合GI方程的孤子仍然基于 $\bar{\partial }$通过选择特殊的光谱变换矩阵求等式。进一步获得了明确的一孤子和二孤子解。GI方程的结果可以作为特殊的还原而从上面给出的结论中恢复。