Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation

被引：68

作者：

Zhang, Yongshuai ^{[1
]}

Cheng, Yi ^{[1
]}

He, Jingsong ^{[2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2017年 / 24卷 / 02期

关键词：

Riemann-Hilbert problem; vector Gerdjikov-Ivanov equation; asymptotic analysis; soliton; KORTEWEG-DEVRIES EQUATION; DARBOUX TRANSFORMATION;

D O I：

10.1080/14029251.2017.1313475

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Riemann-Hilbert method for initial problem of the vector Gerdjikov-Ivanov equation, and obtain the formula for its N-soliton solution, which is expressed as a ratio of (N+1) x (N+1) determinant and N x N determinant. Furthermore, by applying asymptotic analysis, the simple elastic interactions of N-soliton are confirmed, and the shifts of phase and position are also explicitly displayed.

引用

页码：210 / 223

页数：14

共 26 条

[11] METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION [J].

GARDNER, CS ;

GREENE, JM ;

KRUSKAL, MD ;

MIURA, RM .

PHYSICAL REVIEW LETTERS, 1967, 19 (19) :1095-&

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

Geng, Xianguo ;

Wu, Jianping .

WAVE MOTION, 2016, 60 :62-72

[13]

Gerdjikov V. S., 1983, Bulgarian Journal of Physics, V10, P130

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

Guo, Boling ;

Ling, Liming .

JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (07)

[15] The higher order rogue wave solutions of the Gerdjikov-Ivanov equation [J].

Guo, Lijuan ;

Zhang, Yongshuai ;

Xu, Shuwei ;

Wu, Zhiwei ;

He, Jingsong .

PHYSICA SCRIPTA, 2014, 89 (03)

[16] TRANSMISSION OF STATIONARY NONLINEAR OPTICAL PULSES IN DISPERSIVE DIELECTRIC FIBERS .1. ANOMALOUS DISPERSION [J].

HASEGAWA, A ;

TAPPERT, F .

APPLIED PHYSICS LETTERS, 1973, 23 (03) :142-144

[17] SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRODINGER HIERARCHY AND ITS SIMILARITY REDUCTION [J].

Kakei, Saburo ;

Kikuchi, Tetsuya .

GLASGOW MATHEMATICAL JOURNAL, 2005, 47A :99-107

[18] The inverse scattering transform and squared eigenfunctions for a degenerate 3 x 3 operator [J].

Kaup, D. J. ;

Yang, Jianke .

INVERSE PROBLEMS, 2009, 25 (10)

[19] EXACT-SOLUTIONS TO HIGHER-ORDER NONLINEAR EQUATIONS THROUGH GAUGE TRANSFORMATION [J].

KUNDU, A .

PHYSICA D, 1987, 25 (1-3) :399-406

[20]

Novikov S. P., 1984, THEORY SOLITONS INVE

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