Based on the zero curvature equation as well as recursive operators, a new spectral problem and the associated multi-component Gerdjikov–Ivanov (GI) integrable hierarchy are studied. The bi-Hamiltonian structure of the multi-component GI hierarchy is obtained by the trace identity which shows that the multi-component GI hierarchy is integrable. In order to solve the multi-component GI system, a class of Riemann–Hilbert (RH) problem is constructed with the zero boundary. When the jump matrix $G$ is an identity matrix, the $N$-soliton solutions of the integrable system are explicitly gained. At last, the one-, two- and $N$-soliton solutions are explicitly shown.

基于零曲率方程以及递归算子，研究了一个新的光谱问题以及相关的多分量Ge​​rdjikov-Ivanov（GI）可积层次。通过跟踪标识获得了多组分GI层次结构的双哈密顿结构，表明痕迹多组分GI层次结构是可集成的。为了解决多分量GI系统，构造了一类零边界的Riemann-Hilbert（RH）问题。当跳矩阵$G$ 是一个单位矩阵， $ñ$明确获得了可积系统的孤子解。最后，一，二和$ñ$-soliton解决方案已明确显示。