The N-soliton solutions to the Hirota and Maxwell-Bloch equation via the Riemann-Hilbert approach

被引：2

作者：

Li, Jian ^{[1
]}

Xia, Tiecheng ^{[1
]}

Wei, Hanyu ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Zhoukou Normal Univ, Coll Math & Stat, Zhoukou 466001, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MODERN PHYSICS B | 2021年 / 35卷 / 11期

关键词：

Hirota and Maxwell-Bloch equation; Riemann-Hilbert problem; N-soliton solutions; Lax pair; integrable equation; NONLINEAR SCHRODINGER-EQUATION; LONG-TIME ASYMPTOTICS; DE-VRIES EQUATION;

D O I：

10.1142/S0217979221501538

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, we study the N-soliton solutions for the Hirota and Maxwell-Bloch equation with physical meaning. From the Lax pair and Volterra integral equations, the Riemann-Hilbert problem of this integrable equation is constructed. By solving the matrix Riemann-Hilbert problem with the condition of no reflecting, the N-soliton solutions for the Hirota and Maxwell-Bloch equation are obtained explicitly. Finally, we simulate the three-dimensional diagram of |E| with 2-soliton solutions and the motion trajectory of t-axis in the case of different z.

引用

页数：9

共 22 条

[1] The N-soliton solutions for the matrix modified Korteweg-de Vries equation via the Riemann-Hilbert approach [J].

Chen, Xiaotong ;

Zhang, Yi ;

Liang, Jianli ;

Wang, Rui .

EUROPEAN PHYSICAL JOURNAL PLUS, 2020, 135 (07)

[2] A STEEPEST DESCENT METHOD FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS - ASYMPTOTICS FOR THE MKDV EQUATION [J].

DEIFT, P ;

ZHOU, X .

ANNALS OF MATHEMATICS, 1993, 137 (02) :295-368

[3] The nonlinear Schrodinger equation on the half-line [J].

Fokas, AS ;

Its, AR ;

Sung, LY .

NONLINEARITY, 2005, 18 (04) :1771-1822

[4] A unified transform method for solving linear and certain nonlinear PDEs [J].

Fokas, AS .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1962) :1411-1443

[5] Riemann-Hilbert approach and N-soliton solutions for a generalized Sasa-Satsuma equation [J].

Geng, Xianguo ;

Wu, Jianping .

WAVE MOTION, 2016, 60 :62-72

[6] Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrodinger equation [J].

Guo, Boling ;

Ling, Liming .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (07)

[7] Supplementary variable method for structure-preserving approximations to partial differential equations with deduced equations [J].

Hong, Qi ;

Li, Jun ;

Wang, Qi .

APPLIED MATHEMATICS LETTERS, 2020, 110

[8] Riemann-Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line [J].

Hu, Bei-Bei ;

Xia, Tie-Cheng ;

Ma, Wen-Xiu .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 332 :148-159

[9] Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber [J].

Kang, Zhou-Zheng ;

Xia, Tie-Cheng .

CHINESE PHYSICS LETTERS, 2019, 36 (11)

[10] Multi-soliton solutions for the coupled modified nonlinear Schrodinger equations via Riemann-Hilbert approach [J].

Kang, Zhou-Zheng ;

Xia, Tie-Cheng ;

Ma, Xi .

CHINESE PHYSICS B, 2018, 27 (07)

← 1 2 3 →