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

[11] Rogue waves in nonlinear hyperbolic systems (shallow-water framework) [J].

Didenkulova, Ira ;

Pelinovsky, Efim .

NONLINEARITY, 2011, 24 (03) :R1-R18

[12] Note on breather type solutions of the NLS as models for freak-waves [J].

Dysthe, KB ;

Trulsen, K .

PHYSICA SCRIPTA, 1999, T82 :48-52

[13] Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing [J].

Fedun, V. ;

Ruderman, M. S. ;

Erdelyi, R. .

PHYSICS LETTERS A, 2008, 372 (39) :6107-6110

[14] ON A CLASS OF PHYSICALLY IMPORTANT INTEGRABLE EQUATIONS [J].

FOKAS, AS .

PHYSICA D-NONLINEAR PHENOMENA, 1995, 87 (1-4) :145-150

[15] Nonlinear Schrodinger equation: Generalized Darboux transformation and rogue wave solutions [J].

Guo, Boling ;

Ling, Liming ;

Liu, Q. P. .

PHYSICAL REVIEW E, 2012, 85 (02)

[16] Determinant representation of Darboux transformation for the AKNS system [J].

He Jingsong ;

Zhang Ling ;

Cheng Yi ;

Li Yishen .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (12) :1867-1878

[17] New Types of Rogue Wave in an Erbium-Doped Fibre System [J].

He, Jingsong ;

Xu, Shuwei ;

Porsezian, Kuppuswamy .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2012, 81 (03)

[18] Generalization of the Kaup-Newell inverse scattering formulation and Darboux transformation [J].

Imai, K .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1999, 68 (02) :355-359

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

KAUP, DJ ;

NEWELL, AC .

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

[20] Physical mechanisms of the rogue wave phenomenon [J].

Kharif, C ;

Pelinovsky, E .

EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2003, 22 (06) :603-634

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