Multi-component generalized Gerdjikov–Ivanov integrable hierarchy and its Riemann–Hilbert problem

Abstract

In this paper, the multi-component generalized Gerdjikov–Ivanov integrable hierarchy is obtained by means of the corresponding spectral problem and the zero curvature equation. With the help of trace identity, the multi-Hamiltonian structures of this integrable hierarchy are investigated. Based on the spectral problem, a specific Riemann–Hilbert problem is formulated for the generalized Gerdjikov–Ivanov integrable hierarchy. When the jump matrix is a unit matrix, through solving this Riemann–Hilbert problem, the N-soliton solutions can be derived.