Multi-component Gerdjikov-Ivanov system and its Riemann-Hilbert problem under zero boundary conditions

Based on the zero curvature equation as well as recursive operators, a new spectral problem and the associated multi-component Gerdjikov-Ivanov (GI) integrable hierarchy are studied. The bi-Hamiltonian structure of the multi-component GI hierarchy is obtained by the trace identity which shows that the multi-component GI hierarchy is integrable. In order to solve the multi-component GI system, a class of Riemann-Hilbert (RH) problem is constructed with the zero boundary. When the jump matrix G is an identity matrix, the N-soliton solutions of the integrable system are explicitly gained. At last, the one-, two- and N-soliton solutions are explicitly shown. (C) 2020 Elsevier Ltd. All rights reserved.