In this article, the inverse scattering transform is considered for the Gerdjikov–Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann–Hilbert (RH) method. The formula of the soliton solutions is established by Laurent expansion to the RH problem. The method we used is different from computing solution with simple poles since the residue conditions here are hard to be obtained. The formula of multiple soliton solutions with one high-order pole and N multiple high-order poles are obtained, respectively. The dynamical properties and characteristic for the high-order pole solutions are further analyzed.

中文翻译：

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零/非零背景下Gerdjikov-Ivanov方程的逆散射变换和多重高阶极点解

在本文中，通过矩阵 Riemann-Hilbert (RH) 方法考虑了具有零和非零边界条件的 Gerdjikov-Ivanov 方程的逆散射变换。孤子解的公式是通过对 RH 问题的洛朗展开式建立的。我们使用的方法不同于用简单的极点计算解，因为这里的残差条件很难获得。分别得到了一个高阶极点和N个高阶极点的多重孤子解的公式。进一步分析了高阶极点解的动力学特性和特性。