Dynamics of nonautonomous rogue waves in Bose–Einstein condensate

Abstract We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

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Nonautonomous solitons, breathers and rogue waves for the Gross–Pitaevskii equation in the Bose–Einstein condensate

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2015.12.011 ◽

2016 ◽

Vol 36 ◽

pp. 457-467 ◽

Cited By ~ 14

Author(s):

Chuan-Qi Su ◽

Yi-Tian Gao ◽

Long Xue ◽

Qi-Min Wang

Keyword(s):

Rogue Waves ◽

Einstein Condensate ◽

Pitaevskii Equation ◽

Bose Einstein Condensate ◽

Bose Einstein

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Matter rogue waves for the three-component Gross–Pitaevskii equations in the spinor Bose–Einstein condensates

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0276 ◽

2018 ◽

Vol 474 (2209) ◽

pp. 20170276 ◽

Cited By ~ 17

Author(s):

Wen-Rong Sun ◽

Lei Wang

Keyword(s):

Modulation Instability ◽

Rogue Wave ◽

Rogue Waves ◽

Einstein Condensate ◽

Rational Solutions ◽

Algebraic Construction ◽

Bose Einstein Condensate ◽

Energy Transfers ◽

Bose Einstein ◽

The Waves

To show the existence and properties of matter rogue waves in an F =1 spinor Bose–Einstein condensate (BEC), we work on the three-component Gross–Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright–dark–bright and bright–bright–bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

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