Super rogue waves in ultracold neutral nonextensive plasmas

2013 ◽  
Vol 79 (6) ◽  
pp. 1049-1056 ◽  
Author(s):  
S. A. EL-TANTAWY ◽  
N. A. EL-BEDWEHY ◽  
W. M. MOSLEM
Keyword(s):  
Rogue Wave ◽  
Perturbation Technique ◽  
Rogue Waves ◽  
Critical Value ◽  
Temperature Ratio ◽  
Rational Solutions ◽  
Existence Region ◽  
Ultracold Neutral Plasmas ◽  
Basic Equations ◽  
Critical Wavenumber

AbstractThe generation of ion-acoustic rogue waves in ultracold neutral plasmas (UNPs) composed of ion fluids and nonextensive electron distribution is investigated. For this purpose, basic equations are reduced to a nonlinear Schrödinger equation (NLSE) using a reductive perturbation technique. The existence region for the rogue waves defined precisely in terms of the critical wavenumber threshold kc. It is found that increasing the nonextensive parameter q would lead to a decrease of kc until q approaches to its critical value qc, then further increase of q beyond qc enhances kc; however, kc shrinks with the increase of the ions effective temperature ratio σ∗. The dependence of the first- and second-order rational solutions profile on the UNP parameters is numerically examined. It is noticed that near to the critical nonextensive parameter qc, the rogue wave amplitude becomes smaller, but it enhances whenever we stepped away from qc. However, the enhancement of the temperature ratio σ∗ and the wavenumber k reduces the envelope rogue wave amplitudes.

Analytic rogue wave-type solutions for the generalized (2+1)-dimensional Boussinesq Equation

2021 ◽  
pp. 2150380
Author(s):  
Xiu-Rong Guo
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Wave Interaction ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Wave Type ◽  
Hirota Bilinear Form ◽  
Basic Facts ◽  
2D And 3D ◽  
Solitary Wave Interaction

Based on the Hirota bilinear form of the generalized (2+1)-dimensional Boussinesq equation, which can be expressed as the shallow water wave mechanism appearing in fluid mechanics, we applied the new polynomial functions to construct the rational solutions and rogue wave-type solutions. Next, the system parameters control on the rational solutions and rogue wave-type solutions were also shown. As a result, we found the following basic facts: (i) these parameters may affect the wave shapes, amplitude, and bright/dark for this considered equation, (ii) the solitary wave interaction rogue waves and triplet rogue wave-type solutions can be viewed on [Formula: see text], [Formula: see text], and [Formula: see text] planes, respectively. Their nonlinear dynamic behaviors were presented by numerical simulation of the 2D- and 3D-plots.

Rogue Wave and Breather Structures with “High Frequency” and “Low Frequency” in 𝒫𝒯-Symmetric Nonlinear Couplers with Gain and Loss

2016 ◽  
Vol 71 (10) ◽  
pp. 961-969 ◽  
Author(s):  
Dang-Jun Yu ◽  
Jie-Fang Zhang
Keyword(s):  
High Frequency ◽  
Rogue Wave ◽  
Low Frequency ◽  
Zero Solution ◽  
Rogue Waves ◽  
Transformation Method ◽  
Rational Solutions ◽  
Plane Wave Solution ◽  
Gain And Loss ◽  
Basic Characteristics

AbstractBased on the modified Darboux transformation method, starting from zero solution and the plane wave solution, the hierarchies of rational solutions and breather solutions with “high frequency” and “low frequency” of the coupled nonlinear Schrödinger equation in parity-time symmetric nonlinear couplers with gain and loss are constructed, respectively. From these results, some basic characteristics of multi-rogue waves and multi-breathers are studied. Based on the property of rogue wave as the “quantum” of pattern structure in rogue wave hierarchy, we further study the novel structures of the superposed Akhmediev breathers, Kuznetsov-Ma solitons and their combined structures. It is expected that these results may give new insight into the context of the optical communications and Bose-Einstein condensations.

A variable coefficient nonlinear Schrödinger equation: localized waves on the plane wave background and their dynamics

2019 ◽  
Vol 33 (10) ◽  
pp. 1850121 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Variable Coefficient ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Plane Wave Background ◽  
Localized Waves ◽  
Similarity Reductions

In this work, a variable coefficient nonlinear Schrödinger (vc-NLS) equation is under investigation, which can describe the amplification or absorption of pulses propagating in an optical fiber with distributed dispersion and nonlinearity. By means of similarity reductions, a similar transformation helps us to relate certain class of solutions of the standard NLS equation to the solutions of integrable vc-NLS equation. Furthermore, we analytically consider nonautonomous breather wave, rogue wave solutions and their interactions in the vc-NLS equation, which possess complicated wave propagation in time and differ from the usual breather waves and rogue waves. Finally, the main characteristics of the rational solutions are graphically discussed. The parameters in the solutions can be used to control the shape, amplitude and scale of the rogue waves.

Rogue Waves and Hybrid Solutions of the Boussinesq Equation

2017 ◽  
Vol 72 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Ji-Guang Rao ◽  
Yao-Bin Liu ◽  
Chao Qian ◽  
Jing-Song He
Keyword(s):  
Boussinesq Equation ◽  
Rogue Wave ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Hirota Bilinear

AbstractThe rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.

scholarly journals Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200842
Author(s):  
Wen-Rong Sun ◽  
Lei Liu ◽  
P. G. Kevrekidis
Keyword(s):  
Rogue Wave ◽  
Background Level ◽  
Rogue Waves ◽  
Background Field ◽  
High Peak ◽  
Peak Amplitude ◽  
Rational Solutions ◽  
Fourth Degree ◽  
Coupled Equations ◽  
Coherent Coupling

We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrödinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness is confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field .

Breathers, rogue waves and their dynamics in a (2+1)-dimensional nonlinear Schrödinger equation

2020 ◽  
Vol 34 (23) ◽  
pp. 2050234
Author(s):  
Yong Chen ◽  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Plane Wave Solution ◽  
Nonlinear Schrödinger ◽  
Wave Phenomena

Under investigation in this paper is a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which is a generalization of the standard nonlinear Schrödinger equation. By means of the modified Darboux transformation, the hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Furthermore, the main characteristics of the nonlinear waves including the Akhmediev breathers, Kuznetsov–Ma solitons, and their combined structures are graphically discussed. Our results would be of much importance in enriching and explaining rogue wave phenomena in nonlinear wave fields.

scholarly journals Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Zhonglong Zhao ◽  
Lingchao He ◽  
Yubin Gao
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Wave Form ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Lump Solutions ◽  
First Order ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Lump Wave

In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8-lump solutions are presented, respectively. The 3-lump wave has a “triangular” structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation.

Rational Solutions and Rogue Waves in Nonlinear Schrödinger Equation With Varying Coefficients

2014 ◽  
Author(s):  
Ni Song ◽  
Wei Zhang ◽  
Sha. Zhou ◽  
Qian Wang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Formation Mechanisms ◽  
Rational Solutions ◽  
Nonlinear Schrödinger ◽  
Varying Coefficients

The similarity transformation and direct ansatz are applied to obtain rogue wave solutions of nonlinear Schrödinger equation with varying coefficients. These obtained solutions can be used to describe the possible formation mechanisms for optical rogue wave phenomenon in optical fibres. Moreover their dynamical behaviors are exhibited for chosen different functions. This will further excite the possibility of relative researchers and potential applications of rogue waves in other related fields.

scholarly journals Matter rogue waves for the three-component Gross–Pitaevskii equations in the spinor Bose–Einstein condensates

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170276 ◽  
Author(s):  
Wen-Rong Sun ◽  
Lei Wang
Keyword(s):  
Modulation Instability ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Einstein Condensate ◽  
Rational Solutions ◽  
Algebraic Construction ◽  
Bose Einstein Condensate ◽  
Energy Transfers ◽  
Bose Einstein ◽  
The Waves

To show the existence and properties of matter rogue waves in an F =1 spinor Bose–Einstein condensate (BEC), we work on the three-component Gross–Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright–dark–bright and bright–bright–bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Rational and semi-rational solutions for the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

2019 ◽  
Vol 33 (25) ◽  
pp. 1950296 ◽  
Author(s):  
Ya-Si Deng ◽  
Bo Tian ◽  
Yan Sun ◽  
Chen-Rong Zhang ◽  
Cong-Cong Hu
Keyword(s):  
Water Waves ◽  
Boussinesq Equation ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Different Shapes ◽  
Lump Wave ◽  
Kink Soliton

Nonlinear waves are seen in nature, such as the water waves and plasma waves. Investigated in this paper is a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Based on the bilinear method, we get the rational solutions, which are different from the published ones, semi-rational solutions and breather-type kink soliton solutions. Through the rational solutions, we observe two types of waves: the lump waves and line rogue waves. The semi-rational solutions depict two types of interactions: (1) The fusion or fission between the lump wave and soliton; (2) The interaction between the line rogue wave and soliton. During the interaction between the line rogue wave and soliton, the line rogue wave evolves with three different shapes: the bright rogue waves, bright–dark rogue waves and dark rogue waves. Via the breather-type kink soliton solutions, we observe the breather-soliton mixture.

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