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

被引：8
|
作者：
Zhang, Yong [1 ,2 ]
Dong, Huan-He [1 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[2] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2021年 / 60卷
基金：
中国国家自然科学基金;
关键词：
Multi-component Gerdjikov-Ivanov equation; Bi-Hamiltonian structure; Riemann-Hilbert problem; N-soliton solution; HAMILTONIAN STRUCTURES; NONLINEAR EQUATIONS; SEMIDIRECT SUMS; TRANSFORMATION; EVOLUTION; WAVES;
D O I：
10.1016/j.nonrwa.2020.103279
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：21
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