Application of the Riemann-Hilbert method to the vector modified Korteweg-de Vries equation

被引：22
|
作者：
Wang, Xiu-Bin [1 ]
Han, Bo [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China
来源：
NONLINEAR DYNAMICS | 2020年 / 99卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Inverse scattering transform; Riemann-Hilbert problem; Multi-soliton solutions; NONLINEAR SCHRODINGER-EQUATION; N-SOLITON SOLUTIONS; BOUNDARY VALUE-PROBLEMS; LONG-TIME ASYMPTOTICS; OPTICAL SOLITONS; BRIGHT; LUMP; COLLISIONS; SYMMETRY; WAVES;
D O I：
10.1007/s11071-019-05359-x
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
Under investigation in this paper is the inverse scattering transform of the vector modified Korteweg-de Vries (vmKdV) equation, which can be reduced to several integrable systems. For the direct scattering problem, the spectral analysis is performed for the equation, from which a Riemann-Hilbert problem is well constructed. For the inverse scattering problem, the Riemann-Hilbert problem corresponding to the reflection-less case is solved. Furthermore, as applications, three types of multi-soliton solutions are found. Finally, some figures are presented to discuss the soliton behaviors of the vmKdV equation.
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页码：1363 / 1377
页数：15
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