Rogue Waves of the Fokas-Lenells Equation

被引：122

作者：

He, Jingsong ^{[1
]}

Xu, Shuwei ^{[1
]}

Porsezian, Kuppuswamy ^{[2
]}

机构：

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

[2] Pondicherry Univ, Dept Phys, Pondicherry 605014, India

来源：

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN | 2012年 / 81卷 / 12期

关键词：

Fokas-Lenells equation; Darboux transformation; breather solution; rogue wave; NONLINEAR SCHRODINGER-EQUATION; DARBOUX TRANSFORMATION; MODULATION INSTABILITY; FREAK-WAVES; SOLITON;

D O I：

10.1143/JPSJ.81.124007

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Fokas-Lenells (FL) equation arises as a model equation which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order [in the leading asymptotic order the nonlinear Schrodinger (NLS) equation results]. Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. When certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.

引用

页数：4

共 42 条

[1]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[2] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE [J].

ABLOWITZ, MJ ;

KAUP, DJ ;

NEWELL, AC ;

SEGUR, H .

PHYSICAL REVIEW LETTERS, 1973, 31 (02) :125-127

[3] How to excite a rogue wave [J].

Akhmediev, N. ;

Soto-Crespo, J. M. ;

Ankiewicz, A. .

PHYSICAL REVIEW A, 2009, 80 (04)

[4] Extreme waves that appear from nowhere: On the nature of rogue waves [J].

Akhmediev, N. ;

Soto-Crespo, J. M. ;

Ankiewicz, A. .

PHYSICS LETTERS A, 2009, 373 (25) :2137-2145

[5] Waves that appear from nowhere and disappear without a trace [J].

Akhmediev, N. ;

Ankiewicz, A. ;

Taki, M. .

PHYSICS LETTERS A, 2009, 373 (06) :675-678

[6] Rogue waves and rational solutions of the nonlinear Schroumldinger equation [J].

Akhmediev, Nail ;

Ankiewicz, Adrian ;

Soto-Crespo, J. M. .

PHYSICAL REVIEW E, 2009, 80 (02)

[7] MODULATION INSTABILITY AND PERIODIC-SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION [J].

AKHMEDIEV, NN ;

KORNEEV, VI .

THEORETICAL AND MATHEMATICAL PHYSICS, 1986, 69 (02) :1089-1093

[8] Rogue waves and rational solutions of the Hirota equation [J].

Ankiewicz, Adrian ;

Soto-Crespo, J. M. ;

Akhmediev, Nail .

PHYSICAL REVIEW E, 2010, 81 (04)

[9] Granularity and Inhomogeneity Are the Joint Generators of Optical Rogue Waves [J].

Arecchi, F. T. ;

Bortolozzo, U. ;

Montina, A. ;

Residori, S. .

PHYSICAL REVIEW LETTERS, 2011, 106 (15)

[10] Rogue Wave Observation in a Water Wave Tank [J].

Chabchoub, A. ;

Hoffmann, N. P. ;

Akhmediev, N. .

PHYSICAL REVIEW LETTERS, 2011, 106 (20)

← 1 2 3 4 5 →