scholarly journals Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Xin Wang ◽  
Lei Wang ◽  
Jiao Wei ◽  
Bowen Guo ◽  
Jingfeng Kang
Keyword(s):  
Rogue Wave ◽  
Laser Pulses ◽  
Rogue Waves ◽  
Fixed Number ◽  
Second Order ◽  
Ultrashort Laser Pulses ◽  
Resonant Medium ◽  
Schur Polynomials ◽  
Rogue Wave Solution ◽  
Integrable Generalization

The coupled Maxwell–Bloch (CMB) system is a fundamental model describing the propagation of ultrashort laser pulses in a resonant medium with coherent three-level atomic transitions. In this paper, we consider an integrable generalization of the CMB equations with the defocusing case. The CMB hierarchy is derived with the aid of a 3 × 3 matrix eigenvalue problem and the Lenard recursion equation, from which the defocusing CMB model is proposed as a special reduction of the general CMB equations. The n -fold Darboux transformation as well as the multiparametric n th-order rogue wave solution of the defocusing CMB equations are put forward in terms of Schur polynomials. As an application, the explicit rogue wave solutions from first to second order are presented. Apart from the traditional dark rogue wave, bright rogue wave and four-petalled rogue wave, some novel rogue wave structures such as the dark four-peaked rogue wave and the double-ridged rogue wave are found. Moreover, the second-order rogue wave triplets which contain a fixed number of these rogue waves are shown.

scholarly journals Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Bo Xu ◽  
Yufeng Zhang ◽  
Sheng Zhang
Keyword(s):  
Partial Derivative ◽  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Second Order ◽  
Coordinate Plane ◽  
Nls Equation ◽  
Wave Solutions ◽  
Rogue Wave Solution ◽  
Rogue Wave Solutions

To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger (NLS) equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

Characteristics of the breathers, rogue waves and soliton waves in a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov equation

2019 ◽  
Vol 33 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Rogue Wave ◽  
Solitary Wave Solution ◽  
Dynamical Behavior ◽  
Rogue Waves ◽  
Bilinear Forms ◽  
Wave Fields ◽  
Rogue Wave Solution ◽  
Bell’S Polynomials

In this work, a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov (GNNV) equation, which can be reduced to several integrable equations, is under investigation. By virtue of Bell’s polynomials, an effective and straightforward way is presented to succinctly construct its two bilinear forms. Furthermore, based on the bilinear formalism and the extended homoclinic test, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. The results can be used to enrich the dynamical behavior of the (2 + 1)-dimensional nonlinear wave fields.

scholarly journals New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Changfu Liu ◽  
Chuanjian Wang ◽  
Zhengde Dai ◽  
Jun Liu
Keyword(s):  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Periodic Wave ◽  
Homoclinic Solution ◽  
Test Method ◽  
New Family ◽  
Higher Dimensional ◽  
Rogue Wave Solution ◽  
Extreme Behavior

A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and DSII equations are obtained using the extended homoclinic test method and homoclinic breather limit method (HBLM), respectively. Moreover, rogue wave solution is exhibited as period of periodic wave in homoclinic breather wave approaches to infinite. This result shows that rogue wave can be generated by extreme behavior of homoclinic breather wave for higher dimensional nonlinear wave fields.

Generalized Darboux transformation and rogue wave solution of the coherently-coupled nonlinear Schrödinger system

2016 ◽  
Vol 30 (13) ◽  
pp. 1650208 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Sha-Sha Yuan ◽  
Yue Wang
Keyword(s):  
Darboux Transformation ◽  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Rogue Wave Solution ◽  
Bright Soliton Solution ◽  
Generalized Darboux Transformation ◽  
Schrödinger System

In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS system.

Generalized Darboux transformation and the higher-order semirational solutions for a non-linear Schrödinger system in a birefringent fiber

2021 ◽  
pp. 2150013
Author(s):  
Dan-Yu Yang ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yu-Qiang Yuan ◽  
Chen-Rong Zhang ◽  
...  
Keyword(s):  
Darboux Transformation ◽  
Phase Modulation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Four Wave Mixing ◽  
Second Order ◽  
Wave Mixing ◽  
Third Order ◽  
Non Linear ◽  
Schrödinger System

Temporal birefringent effects in the fibers change the crosstalk behaviors inside and between the fiber cores in the linear and non-linear optical power areas. This paper studies a non-linear Schrödinger system with the four-wave mixing term, which describes the optical solitons in a birefringent fiber. We construct the generalized Darboux transformation, and acquire the higher-order semirational solutions consisting of the second- and third-order semirational solutions, which represent the complex amplitudes of the electric fields in the two orthogonal polarizations. We acquire the interactions between/among the two/three solitons. Such interactions are elastic and generate the rogue waves around the interacting regions. We obtain the interactions among the second-/third-order rogue waves and two/three solitons, respectively. When [Formula: see text] decreases, amplitude of the second-order rogue wave increases, with [Formula: see text] and [Formula: see text] accounting for the self-phase modulation and cross-phase modulation, respectively, while [Formula: see text] representing the four-wave mixing effect. With [Formula: see text] kept invariant, when [Formula: see text] increases and [Formula: see text], amplitudes of the second-order rogue wave and two bright solitons increase, while when [Formula: see text] increases and [Formula: see text], amplitudes of the second-order rogue wave and two dark solitons increase, with [Formula: see text] and [Formula: see text] being the constants.

scholarly journals Terahertz Waveforms Generated by Second-Order Nonlinear Polarization in GaAs/AlAs Coupled Multilayer Cavities Using Ultrashort Laser Pulses

2013 ◽  
Vol 5 (3) ◽  
pp. 6500308-6500308 ◽  
Author(s):  
T. Kitada ◽  
S. Katoh ◽  
T. Takimoto ◽  
Y. Nakagawa ◽  
K. Morita ◽  
...  
Keyword(s):  
Laser Pulses ◽  
Second Order ◽  
Ultrashort Laser Pulses ◽  
Nonlinear Polarization ◽  
Ultrashort Laser

scholarly journals Sensitivity enhancement by increasing the nonlinear crystal length in second-order autocorrelators for ultrashort laser pulses measurement

2019 ◽  
Vol 437 ◽  
pp. 367-372
Author(s):  
Sebastián Jarabo ◽  
Enrique Rodríguez-Martín ◽  
José E. Saldaña-Díaz ◽  
Francisco J. Salgado-Remacha
Keyword(s):  
Nonlinear Crystal ◽  
Laser Pulses ◽  
Sensitivity Enhancement ◽  
Second Order ◽  
Ultrashort Laser Pulses ◽  
Crystal Length ◽  
Ultrashort Laser

Solitons and rogue waves for a nonlinear system in the geophysical fluid

2016 ◽  
Vol 30 (35) ◽  
pp. 1650412 ◽  
Author(s):  
Xi-Yang Xie ◽  
Bo Tian ◽  
Lei Liu ◽  
Xiao-Yu Wu ◽  
Yan Jiang
Keyword(s):  
Nonlinear System ◽  
Wave Packet ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Second Order ◽  
Basic Flow ◽  
Mean Flow ◽  
First Order ◽  
Derived Properties

In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with [Formula: see text], which reflects the collision between the wave packet and mean flow, [Formula: see text], which measures the state of the basic flow, and group velocity [Formula: see text]. [Formula: see text] is observed to affect the amplitudes of the solitons, and [Formula: see text] can influence the solitons’ traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. [Formula: see text] has no effects on A, which is the amplitude of the wave packet, but with the increase of [Formula: see text], amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When [Formula: see text] is chosen differently, A and B do not keep their shapes invariant. With the value of [Formula: see text] increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with [Formula: see text] increasing, amplitude of B decreases, but [Formula: see text] has no effects on A. Collision features of A and B alter with the value of [Formula: see text] changing. When we make the value of [Formula: see text] larger, amplitudes of A and B increase.

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