Multi-component Gerdjikov–Ivanov system and its Riemann–Hilbert problem under zero boundary conditions. (August 2021)

• Record Type: Journal Article
• Authors: Zhang, Yong; Dong, Huan-He
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: Multi-component Gerdjikov–Ivanov equation -- Bi-Hamiltonian structure -- Riemann–Hilbert problem -- N-soliton solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103279
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.