RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS

被引：0
作者：
马文秀
机构：
[1] Department of Mathematics and Statistics, University of South Florida
[2] College of Mathematics and Physics, Shanghai University of Electric Power
[3] College of Mathematics and Systems Science, Shandong University of Science and Technology
[4] Department of Mathematics, King Abdulaziz University
[5] Department of Mathematics, Zhejiang Normal University
[6] International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus
来源：
Acta Mathematica Scientia | 2019年 / 02期
关键词：
integrable hierarchy; Riemann-Hilbert problem; soliton solution;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
Based on a 4 x 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.
引用
收藏
页码：509 / 523
页数：15
相关论文
共 50 条
[21]   On the origins of Riemann-Hilbert problems in mathematics* [J].
Bothner, Thomas .
NONLINEARITY, 2021, 34 (04) :R1-R73
[22]   Separation Principles and Riemann-Hilbert Problems [J].
Gunter Semmler ;
Elias Wegert .
Computational Methods and Function Theory, 2003, 2 (1) :175-190
[23]   Asymptotic expansions for Riemann-Hilbert problems [J].
Qiu, W. -Y. ;
Wong, R. .
ANALYSIS AND APPLICATIONS, 2008, 6 (03) :269-298
[24]   Riemann-Hilbert Method Equipped with Mixed Spectrum for N-Soliton Solutions of New Three-Component Coupled Time-Varying Coefficient Complex mKdV Equations [J].
Zhang, Sheng ;
Wang, Xianghui ;
Xu, Bo .
FRACTAL AND FRACTIONAL, 2024, 8 (06)
[25]   Schwarz, Riemann, Riemann-Hilbert Problems and Their Connections in Polydomains [J].
Mohammed, Alip .
PSEUDO-DIFFERENTIAL OPERATORS: COMPLEX ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 205 :143-166
[26]   Matrix Riemann-Hilbert problems and factorization on Riemann surfaces [J].
Camara, M. C. ;
dos Santos, A. F. ;
dos Santos, Pedro F. .
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (01) :228-254
[27]   Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions [J].
Li, Sha ;
Xia, Tiecheng ;
Wei, Hanyu .
CHINESE PHYSICS B, 2023, 32 (04)
[28]   Exact multi-soliton solutions of the KdV equation with a source: Riemann-Hilbert formulation [J].
Zhu, Dinghao ;
Zhu, Xiaodong .
APPLIED MATHEMATICS LETTERS, 2024, 149
[29]   N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method [J].
Xu, Si-Qi ;
Geng, Xian-Guo .
CHINESE PHYSICS B, 2018, 27 (12)
[30]   A two-component modified Korteweg-de Vries equation: Riemann-Hilbert problem and multi-soliton solutions [J].
Yan, Xue-Wei .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (03) :569-579
12345