零/非零背景下Gerdjikov-Ivanov方程的逆散射变换和多个高阶极点解
Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background
摘要：
利用矩阵Riemann-Hilbert（RH）方法，研究了具有零和非零边界条件的Gerdjikov-Ivanov方程的逆散射变换.通过对RH问题的Laurent展开，建立了孤立子解的计算公式.由于留数条件难以得到，所以我们采用的方法与用简单极点计算解的方法不同。分别得到了具有一个高阶极点和$N$多个高阶极点的多孤子解的计算公式。进一步分析了高阶极点解的动力学性质和特征。
英文摘要：
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 are 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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
