  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.
