High-order soliton matrices for Sasa-Satsuma equation via local Riemann-Hilbert problem

被引：62

作者：

Yang, Bo ^{[1
]}

Chen, Yong ^{[1
]}

机构：

[1] East China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2019年 / 45卷

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Riemann-Hilbert problem; Darboux transformation; High-order soliton solution; Asymptotic analysis; NONLINEAR SCHRODINGER-EQUATION; DISPERSIVE DIELECTRIC FIBERS; OPTICAL PULSES; TRANSMISSION; PROPAGATION;

D O I：

10.1016/j.nonrwa.2018.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A study of high-order soliton matrices for Sasa-Satsuma equation in the framework of the Riemann-Hilbert problem approach is presented. Through a standard dressing procedure, soliton matrices for simple zeros and elementary high-order zeros in the Riemann-Hilbert problem for Sasa-Satsuma equation are constructed, respectively. It is noted that pairs of zeros are simultaneously tackled in the situation of the high-order zeros, which is different from other NLS-type equation. Furthermore, the generalized Darboux transformation for Sasa-Satsuma equation is also presented. Moreover, collision dynamics along with the asymptotic behavior for the two-solitons are analyzed, and long time asymptotic estimations for the high-order one-soliton are concretely calculated. In this case, two double-humped solitons with nearly equal velocities and amplitudes can be observed. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：918 / 941

页数：24

共 33 条

[11] N-SOLITON INTERACTION IN OPTICAL FIBERS - THE MULTIPLE-POLE CASE [J].

GAGNON, L ;

STIEVENART, N .

OPTICS LETTERS, 1994, 19 (09) :619-621

[12] Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions [J].

Gilson, C ;

Hietarinta, J ;

Nimmo, J ;

Ohta, Y .

PHYSICAL REVIEW E, 2003, 68 (01) :10-166141

[13] 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

[14] TRANSMISSION OF STATIONARY NONLINEAR OPTICAL PULSES IN DISPERSIVE DIELECTRIC FIBERS .2. NORMAL DISPERSION [J].

HASEGAWA, A ;

TAPPERT, F .

APPLIED PHYSICS LETTERS, 1973, 23 (04) :171-172

[15] EXACT ENVELOPE-SOLITON SOLUTIONS OF A NONLINEAR WAVE-EQUATION [J].

HIROTA, R .

JOURNAL OF MATHEMATICAL PHYSICS, 1973, 14 (07) :805-809

[16] EXACT SOLUTION FOR A DERIVATIVE NON-LINEAR SCHRODINGER EQUATION [J].

KAUP, DJ ;

NEWELL, AC .

JOURNAL OF MATHEMATICAL PHYSICS, 1978, 19 (04) :798-801

[17] NONLINEAR PULSE-PROPAGATION IN A MONOMODE DIELECTRIC GUIDE [J].

KODAMA, Y ;

HASEGAWA, A .

IEEE JOURNAL OF QUANTUM ELECTRONICS, 1987, 23 (05) :510-524

[18] OPTICAL SOLITONS IN A MONOMODE FIBER [J].

KODAMA, Y .

JOURNAL OF STATISTICAL PHYSICS, 1985, 39 (5-6) :597-614

[19] THE ALGEBRAIC REPRESENTATION FOR HIGH ORDER SOLUTION OF SASA-SATSUMA EQUATION [J].

Ling, Liming .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2016, 9 (06) :1975-2010

[20] Dynamic patterns of high-order rogue waves for Sasa-Satsuma equation [J].

Mu, Gui ;

Qin, Zhenyun .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 31 :179-209

← 1 2 3 4 →