Vector rogue waves in binary mixtures of Bose-Einstein condensates

Bludov, Yuliy V.; Konotop, V. V.; Akhmediev, Nail

doi:10.1140/epjst/e2010-01247-6

Cited by 207 publications

(141 citation statements)

References 26 publications

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“…(14) and the star denotes complex conjugate of it. The above expressions can be rewritten as the second derivative of a logarithimic function, namely…”

Section: Gbs As Imbricate Series Of Rwsmentioning

confidence: 99%

“…These waves may arise from the instability of a certain class of initial conditions that tend to grow exponentially and thus have the possibility of increasing up to very high amplitudes, due to modulation instability [13]. Over the years RWs have also been observed in models that arise in the description of multi-component BoseEinstein condensates [14], capillary waves [15], multicomponent plasmas [16] and even in finance [17]. Recently efforts have been made to explain the RW excitation through a nonlinear process.…”

Section: Introductionmentioning

confidence: 99%

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Akhmediev breathers, Ma solitons, and general breathers from rogue waves: A case study in the Manakov system

2013

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We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS) and rogue wave (RW) solutions of the two component nonlinear Schrödinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS and RW solutions. We then consider the RW solution as the starting point and derive AB, MS and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter. Through this two way approach we establish a broader understanding of these rational solutions which will be of interest in a variety of situations.

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“…(14) and the star denotes complex conjugate of it. The above expressions can be rewritten as the second derivative of a logarithimic function, namely…”

Section: Gbs As Imbricate Series Of Rwsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Akhmediev breathers, Ma solitons, and general breathers from rogue waves: A case study in the Manakov system

2013

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“…For instance, consider a system of coupled nonlinear Schrödinger equations (NLSEs) to describe the nonlinear interaction between wave packets in dispersive conservative media. Such coupled systems are of physical relevance in various domains such as nonlinear optics, hydrodynamics, plasma physics, multicomponent Bose-Einstein condensates, and financial systems [1][2][3][4][5]. The first multicomponent NLSE type of model with applications to physics is the well-known Manakov model [6].…”

Section: Introductionmentioning

confidence: 99%

Polarization modulation instability in a Manakov fiber system

et al. 2015

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The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formation. Here, we report experiments in optical fiber that provide evidence of passband and baseband polarization modulation instabilities in a defocusing Manakov system. In the spontaneous regime, we also reveal a unique saturation effect as the pump power increases. We anticipate that such observations may impact the application of this minimal model to describe and understand more complicated phenomena in nature, such as the formation of extreme waves in multicomponent systems.

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“…Followed by this study, some further interesting studies of the nonautonomous NLS models with external potentials have also been made [24][25][26]. Several works have been exclusively devoted to construct soliton, RW and breather solutions of onecomponent BECs [25][26][27][28][29][30][31] and a few studies have been made to identify the vector soliton and RW solutions of two coupled Gross-Pitaevskii equation (GPE) [32][33][34][35][36][37]. Dynamical evolutions of vector solitons and RWs have been investigated through managing related physical variables, see Refs.…”

Section: Introductionmentioning

confidence: 95%

Manipulating localized matter waves in multicomponent Bose-Einstein condensates

et al. 2016

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We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures, namely rogue waves, dark-and bright soliton-rogue wave, and rogue wave-breather-like wave for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Further we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single, two and three composite rogue waves for three component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.

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Vector rogue waves in binary mixtures of Bose-Einstein condensates

Cited by 207 publications

References 26 publications

Akhmediev breathers, Ma solitons, and general breathers from rogue waves: A case study in the Manakov system

Akhmediev breathers, Ma solitons, and general breathers from rogue waves: A case study in the Manakov system

Polarization modulation instability in a Manakov fiber system

Manipulating localized matter waves in multicomponent Bose-Einstein condensates

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