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

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. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, the multi-component generalized Gerdjikov-Ivanov integrable hierarchy is obtained using the spectral problem and zero curvature equation. The multi-Hamiltonian structures of this hierarchy are investigated using trace identity. A specific Riemann-Hilbert problem is formulated for the generalized Gerdjikov-Ivanov integrable hierarchy, and by solving this problem, N-soliton solutions can be derived.