Solitons and Rogue Waves for a Higher-Order Nonlinear Schrödinger–Maxwell–Bloch System in an Erbium-Doped Fiber

2015 ◽  
Vol 70 (11) ◽  
pp. 935-948 ◽  
Author(s):  
Chuan-Qi Su ◽  
Yi-Tian Gao ◽  
Long Xue ◽  
Xin Yu
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Dispersion Parameter ◽  
Frequency Detuning ◽  
Third Order ◽  
First Order ◽  
Third Order Dispersion ◽  
Erbium Doped ◽  
Order Dispersion ◽  
Extant Population

AbstractUnder investigation in this article is a higher-order nonlinear Schrödinger–Maxwell–Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

scholarly journals Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation

2022 ◽  
Author(s):  
Ren Bo ◽  
Shi Kai-Zhong ◽  
Shou-Feng Shen ◽  
Wang Guo-Fang ◽  
Peng Jun-Da ◽  
...  
Keyword(s):  
Bilinear Form ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Ultrashort Pulses ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Femtosecond Regime ◽  
Wave Limit

Abstract In this paper, we investigate the third-order nonlinear Schr\"{o}dinger equation which is used to describe the propagation of ultrashort pulses in the subpicosecond or femtosecond regime. Based on the independent transformation, the bilinear form of the third-order NLSE is constructed. The multiple soliton solutions are constructed by solving the bilinear form. The multi-order rogue waves and interaction between one-soliton and first-order rogue wave are obtained by the long wave limit in multi-solitons. The dynamics of the first-order rogue wave, second-order rogue wave and interaction between one-soliton and first-order rogue wave are presented by selecting the appropriate parameters. In particular parameters, the positions and the maximum of amplitude of rogue wave can be confirmed by the detail calculations.PACS numbers: 02.30.Ik, 05.45.Yv.

scholarly journals Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Song ◽  
W. Zhang ◽  
P. Wang ◽  
Y. K. Xue
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Fifth Order

The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.

Breathers and multiple rogue waves solutions of the (3+1)-dimensional Jimbo–Miwa equation

2021 ◽  
pp. 2150183
Author(s):  
Hong-Yi Zhang ◽  
Yu-Feng Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Hirota Bilinear

In this paper, we construct the breathers of the (3+1)-dimensional Jimbo–Miwa (JM) equation by means of the Hirota bilinear method, then based on the Hirota bilinear method with a new ansatz form, the multiple rogue wave solutions are constructed. Here, we discuss the general breathers, first-order rogue waves, the second-order rogue waves and the third-order rogue waves. Then we draw the 3- and 2-dimensional plots to illustrate the dynamic characteristics of breathers and multiple rogue waves. These interesting results will help us better reveal (3+1)-dimensional JM equation evolution mechanism.

scholarly journals Soliton’s eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

2015 ◽  
Vol 23 (1) ◽  
pp. 143 ◽  
Author(s):  
Gihan Weerasekara ◽  
Akihiro Tokunaga ◽  
Hiroki Terauchi ◽  
Marc Eberhard ◽  
Akihiro Maruta
Keyword(s):  
Optical Fibers ◽  
Wave Phenomenon ◽  
Rogue Wave ◽  
Generation Mechanism ◽  
Third Order ◽  
Third Order Dispersion ◽  
Order Dispersion

scholarly journals Rogue waves in optical fibers in presence of third-order dispersion, self-steepening, and self-frequency shift

2012 ◽  
Vol 30 (1) ◽  
pp. 87 ◽  
Author(s):  
Adrian Ankiewicz ◽  
Jose M. Soto-Crespo ◽  
M. Amdadul Chowdhury ◽  
Nail Akhmediev
Keyword(s):  
Frequency Shift ◽  
Optical Fibers ◽  
Rogue Waves ◽  
Third Order ◽  
Third Order Dispersion ◽  
Order Dispersion

scholarly journals Effect of Streaming Electrons on the Propagation of Electromagnetic Waves in a Magnetised Relativistic Plasma

1994 ◽  
Vol 47 (1) ◽  
pp. 59 ◽  
Author(s):  
SN Paul ◽  
S Chakraborty ◽  
A Roy Chowdhury
Keyword(s):  
Electromagnetic Waves ◽  
Significant Contribution ◽  
Dispersion Relations ◽  
Relativistic Plasma ◽  
Wave Number ◽  
Third Order ◽  
First Order ◽  
Third Order Dispersion ◽  
The Waves ◽  
Order Dispersion

Expressions for the first- and third-order dispersion relations have been derived for circularly polarised waves in a magnetised relativistic plasma containing electron streams. From the first-order dispersion relations it is seen that the waves are split into three parts, one of which is reflected causing the formation of standing waves in the streaming plasma. From the third-order dispersion relations, the expression for the shifts of wave number has been obtained. It is observed that the streaming of electrons has a significant contribution to the wave-number shift of the electromagnetic waves.

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