Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrodinger Equations on the Half-line

被引：39

作者：

Hu, Bei-bei ^{[1
,2
]}

Xia, Tie-cheng ^{[1
]}

Zhang, Ning ^{[3
]}

Wang, Jin-bo ^{[4
]}

机构：

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

[2] Chuzhou Univ, Sch Math & Finance, Chuzhou 239000, Anhui, Peoples R China

[3] Shandong Univ Sci & Technol, Dept Basical Courses, Tai An 271019, Shandong, Peoples R China

[4] Sci & Technol Commun Secur Lab, Chengdu 610041, Sichuan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2018年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Riemann-Hilbert problem; CHNLS equations; initial-boundary value problem; unified transform method; SOLITONS; TRANSFORM;

D O I：

10.1515/ijnsns-2017-0080

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrodinger equations on the half-line. Suppose that the solution {q(1)(x, t), q(2)(x, t)} exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter lambda.

引用

页码：83 / 92

页数：10

共 36 条

[1]

[Anonymous], 2013, P ROY SOC A-MATH PHY, DOI DOI 10.1098/RSPA.2013.0068

[2] Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi's elliptic function method [J].

Bhrawy, A. H. ;

Abdelkawy, M. A. ;

Biswas, Anjan .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (04) :915-925

[3] Quasi-particle theory of optical soliton interaction [J].

Biswas, Anjan ;

Konar, Swapan .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (07) :1202-1228

[4] A Riemann-Hilbert Approach for the Novikov Equation [J].

Boutet De Monvel, Anne ;

Shepelsky, Dmitry ;

Zielinski, Lech .

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2016, 12

[5] Peregrine solitons and algebraic soliton pairs in Kerr media considering space-time correction [J].

Chen, Shihua ;

Song, Lian-Yan .

PHYSICS LETTERS A, 2014, 378 (18-19) :1228-1232

[6] Inverse scattering transform for the Degasperis-Procesi equation [J].

Constantin, Adrian ;

Ivanov, Rossen I. ;

Lenells, Jonatan .

NONLINEARITY, 2010, 23 (10) :2559-2575

[7] Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides [J].

Dai, Chaoqing ;

Wang, Yueyue ;

Zhang, Xiaofei .

OPTICS EXPRESS, 2014, 22 (24) :29862-29867

[8] A Riemann-Hilbert approach for the Degasperis-Procesi equation [J].

de Monvel, Anne Boutet ;

Shepelsky, Dmitry .

NONLINEARITY, 2013, 26 (07) :2081-2107

[9] 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

[10]

Fokas A.S., 2008, SIAM, V78

← 1 2 3 4 →