Riemann-Hilbert approach and the soliton solutions of the discrete mKdV equations

被引：18

作者：

Chen, Meisen ^{[1
,2
]}

Fan, Engui ^{[3
]}

He, Jingsong ^{[1
]}

机构：

[1] Shenzhen Univ, Jingsong He Inst Adv Study, Shenzhen 518060, Peoples R China

[2] Shenzhen Univ, Coll Phys & Optoelect Engn, Shenzhen 518060, Peoples R China

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2023年 / 168卷

基金：

中国国家自然科学基金;

关键词：

Discrete mKdV equation; Inverse scattering transform; Multiple-pole solution; Riemann-Hilbert problem; INVERSE SCATTERING TRANSFORM; LONG-TIME ASYMPTOTICS; TODA LATTICE;

D O I：

10.1016/j.chaos.2023.113209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present the inverse scattering transform of the discrete mKdV equation by the Riemann- Hilbert approach. By its Lax pair, we construct the Jost solution and the reflection coefficients. With these, we assume that there are higher-order zeros for the scattering coefficient ��(��), and construct the corresponding Riemann-Hilbert (RH) problem. In this vein, by the RH problem and the reconstruction formula, we obtain the multiple-pole solutions for the discrete mKdV equations. Compared with simple-pole solutions, multiple-pole solutions possess more complicated profiles.

引用

页数：5

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