Matter rogue waves in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>spinor Bose-Einstein condensate

Qin, Zhenyun; Mu, Gui

doi:10.1103/physreve.86.036601

Cited by 68 publications

(28 citation statements)

References 32 publications

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“…As mentioned before, the rational solutions in class B are equivalent, up to unitary transformations, to one of the solutions derived in Ref. [48]. The other two families of solutions however are new to the best of our knowledge.…”

Section: Clearly Frommentioning

confidence: 53%

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Solitons and rogue waves in spinor Bose-Einstein condensates

Prinari

Biondini

2018

Phys. Rev. E

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We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F=1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

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Section: Clearly Frommentioning

confidence: 53%

“…(Note that Y(x, t, z) =N up (x, t, z) in the notation of Ref. [48]) Relating the integral I in Eq. (A.1) to the asymptotics (A.2), we have…”

Section: Appendix I: Total Spin and Spin Statesmentioning

confidence: 99%

Solitons and rogue waves in spinor Bose-Einstein condensates

Prinari

Biondini

2018

Phys. Rev. E

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“…One begins again with the solution (39) and the following analysis is only slightly more complex. Further, since in a vector system modulational instability may occur in the normal dispersion regime resulting from cross-phase modulation, the corresponding rogue wave solutions are of interest, and the technique presented in this paper is also available for Matrix nonlinear Schrödinger equation [21], these will be reported elsewhere. Also, the novel connection between mulitsolitons and rogue waves revealed here has potentially far-reaching significance, and a topic we will explore in the future.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation

Qin

Grimshaw³

2015

SIAM J. Appl. Math.

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129

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General higher-order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The N th-order semirational solutions containing 3N free parameters are expressed in separation-of-variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structure of rogue waves in this two-component system is richer than that in a one-component system. Our results would be of much importance in understanding and predicting rogue wave phenomena arising in nonlinear and complex systems, including optics, fluid dynamics, Bose-Einstein condensates, and finance. Introduction.It is well known that many nonlinear wave equations of physical interest support solitons, which are localized waves arising from a balance between dispersion and nonlinearity, and which can propagate steadily for a long time. Recently, over the last two decades, it has been recognized that another class of solutions, namely breathers, are also of fundamental importance. Breathers propagate steadily and are localized in either time or space, while being periodic in either space or time. Further, due to their localization properties, breathers have been invoked as models of rogue waves, also called freak waves, which are large amplitude waves which apparently appear without warning and then disappear without trace. While they have been most often found in the context of water waves [1, 2, 3], they have also been found in other physical contexts such as optical fibres [4,5,6].The breather solutions of the focusing nonlinear Schrödinger equation (NLSE) have been widely invoked as models of rogue waves; see the references above and Akhmediev, and Ankiewicz [7], for instance. The NLSE is integrable [8], and many kinds of exact solutions have been found. In particular, the Peregrine breather [9], the Akhmediev breather (AB) [7], and the Kuznetsov-Ma breathers (KM) [10,11] have been associated with rogue waves as the potential outcome of the modulational instability of a plane wave. AB is periodic in space and localized in

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“…These solutions attracted much scientific interest [31][32][33][34][35][36][37][38][39][40][41][42]. The Manakov system [43] is an important integrable two-component NLS system and can be applied to optical as well as hydrodynamic systems [44,45].…”

Section: Vector Eigenfunctions For the Manakov Systemmentioning

confidence: 99%

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

Guo

Zhang

et al. 2014

Proc. R. Soc. A.

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We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

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Matter rogue waves in anF=1spinor Bose-Einstein condensate

Cited by 68 publications

References 32 publications

Solitons and rogue waves in spinor Bose-Einstein condensates

Solitons and rogue waves in spinor Bose-Einstein condensates

Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

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