Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

Abstract. We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.

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“…(16). In the following, we discuss in detail how the dark-dark RW structures get deformed for different forms of diffraction parameter β(z).…”

Section: Characteristics Of Dark-dark Rwsmentioning

confidence: 99%

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

2016

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“…Therefore, it is of high significance to study the dynamics of RWs and breather profiles of the GP equation (1). However only few attempts have been made to identify and analyze the RWs and breather solutions of (1) [35][36][37][38][39][40]. To the best of our knowledge neither higher-order RW solutions (with certain free parameters) nor higher order breather solutions of (1) have been taken up for study.…”

Section: Introductionmentioning

confidence: 99%

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

et al. 2014

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We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) timeindependent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

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“…The scaling behavior is similar to systems that are described by the Kibble-Zurek mechanism (45-47), although a key difference in our system is the presence of dissipation and collapse, which is not part of the Kibble-Zurek scenario. The ability to finely control the interaction between atoms, and the relatively slow timescale for dynamics point toward the study of rogue matterwaves (48,49), analogous to the rogue waves observed in optical systems (50), as a natural extension of this work. Our methods are additionally amenable to studying the formation and propagation of higher-order solitons, such as breathers (51,52).…”

Section: I /(2m)mentioning

confidence: 96%

Formation of matter-wave soliton trains by modulational instability

Hulet

Nguyen

Luo

2017

2017 Conference on Lasers and Electro-Optics Europe &Amp; European Quantum Electronics Conference (CLEO/Europe-EQEC)

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Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By exploiting a shallow zero-crossing of a Feshbach resonance, we characterize modulational instability and its role in the formation of matter-wave soliton trains from a Bose-Einstein condensate. We examine the universal scaling laws exhibited by the system and, through real-time imaging, address a longstanding question of whether the solitons in trains are created with effectively repulsive nearest-neighbor interactions or rather evolve into such a structure. Modulational instability (MI) is a process in which broadband perturbations spontaneouslyseed the nonlinear growth of a nearly monochromatic wave disturbance (1). Owing to its generality, MI plays a role in a variety of different physical systems such as water waves, where it is known as a Benjamin-Feir instability (2); plasma waves; nonlinear optics (3-5); and ultracold atomic gases (6). The nonlinear interaction resulting in MI also supports solitons, which are localized waves whose dispersion is exactly balanced by the nonlinearity (7,8). Thus, the rapid 1 arXiv:1703.04662v2 [cond-mat.quant-gas]

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Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

Cited by 121 publications

References 50 publications

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

Formation of matter-wave soliton trains by modulational instability

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