Odd-soliton solutions and inelastic interaction for the differential-difference nonlinear Schrodinger equation in nonlinear optics

被引：11

作者：

Wen, Xiao-Yong ^{[1
]}

Wang, Deng-Shan ^{[1
]}

机构：

[1] Beijing Informat Sci & Technol Univ, Coll Sci, Dept Math, Beijing 100192, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 244卷

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

The differential-difference nonlinear Schrodinger equation; N-fold Darboux transformation; Odd-soliton solutions; Inelastic interaction; Conservation laws; BACKLUND TRANSFORMATION; DARBOUX TRANSFORMATION; DISCRETE; SYSTEM; MODEL;

D O I：

10.1016/j.amc.2014.07.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlinear Schrodinger equation-type may model diverse physical phenomena in nonlinear optics, plasma physics and fluid mechanics, etc. Under consideration in this paper is the differential-difference nonlinear Schrodinger equation. On the basis of its Lax pair, N-fold Darboux transformation and conservation laws for the differential-difference nonlinear Schrodinger equation are constructed. Odd-soliton solutions in terms of determinant are derived with the resulting Darboux transformation. Figures are plotted to reveal the dynamic features of the solitons. Especially, the inelastic interaction phenomena among the three solitons are discussed for the differential-difference nonlinear Schrodinger equation, which might be useful for understanding some physical phenomena in nonlinear optics. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：598 / 605

页数：8

共 19 条

[1] NONLINEAR EVOLUTION EQUATIONS, CONTINUOUS AND DISCRETE [J].

ABLOWITZ, MJ .

SIAM REVIEW, 1977, 19 (04) :663-684

[2] NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS AND FOURIER-ANALYSIS [J].

ABLOWITZ, MJ ;

LADIK, JF .

JOURNAL OF MATHEMATICAL PHYSICS, 1976, 17 (06) :1011-1018

[3]

ABLOWITZ MJ, 1976, STUD APPL MATH, V55, P213

[4] Approach to first-order exact solutions of the Ablowitz-Ladik equation [J].

Ankiewicz, Adrian ;

Akhmediev, Nail ;

Lederer, Falk .

PHYSICAL REVIEW E, 2011, 83 (05)

[5] Discrete rogue waves of the Ablowitz-Ladik and Hirota equations [J].

Ankiewicz, Adrian ;

Akhmediev, Nail ;

Soto-Crespo, J. M. .

PHYSICAL REVIEW E, 2010, 82 (02)

[6] The management and containment of self-similar rogue waves in the inhomogeneous nonlinear Schrodinger equation [J].

Dai, Chao-Qing ;

Wang, Yue-Yue ;

Tian, Qing ;

Zhang, Jie-Fang .

ANNALS OF PHYSICS, 2012, 327 (02) :512-521

[7] On the gauge equivalent structure of the discrete nonlinear Schrodinger equation [J].

Ding, Q .

PHYSICS LETTERS A, 2000, 266 (2-3) :146-154

[8] Integrability aspects and soliton solutions for an inhomogeneous nonlinear system with symbolic computation [J].

Guo, Rui ;

Tian, Bo .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2012, 17 (08) :3189-3203

[9] RANDOMLY MODULATED DARK SOLITON [J].

KONOTOP, VV ;

VEKSLERCHIK, VE .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (04) :767-785

[10] ON SOLITON CREATION IN THE NONLINEAR SCHRODINGER MODELS - DISCRETE AND CONTINUOUS VERSIONS [J].

KONOTOP, VV ;

VEKSLERCHIK, VE .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (14) :4037-4042

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