Dynamic behaviors of the breather solutions for the AB system in fluid mechanics

Guo, Rui; Hao, Hui-Qin; Zhang, Lingling

doi:10.1007/s11071-013-0998-1

Cited by 154 publications

(36 citation statements)

References 28 publications

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“…In the following, we show that solution (2.1) can describe different kinds of nonlinear wave states depending on the values of velocity [30,41,43].…”

Section: Different Types Of Stationary Nonlinear Wavesmentioning

confidence: 94%

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Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Wang

Zhang

et al. 2016

Nonlinear Dyn

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We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultrashort pulses in nonlinear optics. We show that the breather can be converted into different types of stationary nonlinear waves on constant backgrounds, including the multi-peak soliton, M-shaped soliton, W-shaped soliton and periodic wave. We also investigate the nonlinear interactions between these waves, which display some novel patterns due to the nonpropagating characteristics of the solitons: (1) Two antidark solitons can produce a W-shaped soliton instead of a higher-order antidark one; (2) the interaction between an antidark soliton and a W-shaped soliton can not only generate a higher-order antidark soliton, but also form a W-shaped soliton pair; and (3) the interactions between an oscillation W-shaped soliton and an oscillation M-shaped soliton show the multipeak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.

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“…In the following, we show that solution (2.1) can describe different kinds of nonlinear wave states depending on the values of velocity [30,41,43].…”

Section: Different Types Of Stationary Nonlinear Wavesmentioning

confidence: 94%

“…MI and breather dynamics of System (1.2) have been discussed in Ref. [41]. Reference [42] has studied the envelope solitary waves and periodic waves of System (1.2).…”

Section: Introductionmentioning

confidence: 99%

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Wang

Zhang

et al. 2016

Nonlinear Dyn

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“…6. One can find that if w m = 10, P (2) s is valid approximately when w 0 < 3, which is the case of strong nonlocality. However, P (6) s is valid when w 0 < 8, and P (10) s is still valid when w 0 = 10, which is already the case of general nonlocality.…”

Section: (E)mentioning

confidence: 98%

“…neering [1][2][3][4][5][6][7][8][9][10]. As a class of solutions of nonlinear equations, soliton solutions have unique characters and have been investigated widely.…”

mentioning

confidence: 99%

Dynamics of dipole breathers in nonlinear media with a spatial exponential-decay nonlocality

2015

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By applying the variational approach, the analytical expression of dipole breathers is obtained in nonlinear media with an exponential-decay nonlocal response. The parameters of the width, the amplitude, the phase-front curvature, and the phase of the complex amplitude of the dipole breathers are all given in analytical expressions. It is found that the input power plays a key role in the evolution of dipole breathers, whose magnitude decides the change of the beam width (compressed or broadened) during propagation. The physical reason for the evolution of dipole breathers is analyzed in detail. Numerical simulations are also carried out, and the analytical solutions are in good agreement with numerical simulations.

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“…Bound vector solitons are the self-trapped, localized structures that confine the adjacent vector solitons in a stationary region, and have potential applications in the telecommunications as the data carriers with larger information bits [26]. Physically, breathers arise from the effect of modulation instability, which has been the characteristic feature of various nonlinear dispersive systems, and is associated with dynamical growth and evolution of periodic perturbation on a continuous wave background [27,28]. In practice, breathers need no activation energy and can bridge the gap between highly nonlinear modes and linear phonon modes [29].…”

Section: Introductionmentioning

confidence: 99%

Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

Meng

Qin

2015

Nonlinear Dyn

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A nonlinear Schrödinger equation with self-consistent sources can be used to describe the interaction between an high-frequency electrostatic wave and an ion-acoustic wave in two-component homogeneous plasmas. In this paper, breather and rogue waves solutions for such a system are investigated via the Darboux transformation. The spatially and temporally periodic breathers have been found. When the cubic nonlinearity coefficient and the background amplitude are varied, the propagating trajectories of breather are changed. The interaction between two breathers are also studied, which shows that when the wave numbers are close, the two breathers are partially coalesced. All of the first-, second-, and third-order rogue waves present certain lumps or valleys around a center in the temporal-spatial distribution, and the peak heights of the ion-acoustic waves are more than three times those of the background. However, for the high-frequency electrostatic waves, the values around the centers are less than the background intensity.

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Dynamic behaviors of the breather solutions for the AB system in fluid mechanics

Cited by 154 publications

References 28 publications

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Dynamics of dipole breathers in nonlinear media with a spatial exponential-decay nonlocality

Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

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