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The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, inthis paper, we mainly consider the third-order flow GI equation. In theframework of the Riemann-Hilbert method, through a standard dressing procedure,soliton matrices for simple zeros and elementary high-order zeros in theRiemann-Hilbert problem (RHP) for the third-order flow GI equation areconstructed. Taking advantage of this result, some properties and asymptoticanalysis of single soliton solutions and two-soliton solutions are discussed,and the simple elastic interaction of two-soliton is proved. Compared withsoliton solution of the classical second-order flow, we found that thehigher-order dispersion term affects the propagation velocity, propagationdirection and amplitude of the soliton. Finally, by means of certain limittechnique, the high-order soliton solution matrix for the third-order flow GIequation is derived.

High-order soliton matrix for the third-order flow equation of the Gerdjikov-Ivanov hierarchy through the Riemann-Hilbert method