Journal
NONLINEAR DYNAMICS
Volume 106, Issue 1, Pages 841-854Publisher
SPRINGER
DOI: 10.1007/s11071-021-06851-z
Keywords
Gross-Pitaevskii equation; Darboux transformation; Rogue wave; Breather; Mixed interaction solution; Numerical simulation
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Funding
- National Natural Science Foundation of China [12075034, 11875008]
- Fundamental Research Funds for the Central Universities [2019XD-A09-3]
- Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology [SKL2018KF04]
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In this study, a breather, rogue wave, and mixed interaction structures are identified in the Gross-Pitaevskii equation in Bose-Einstein condensate using the generalized Darboux transformation method, with discussions on the effects of related parameters on rogue wave structures. Numerical simulations confirm the dynamics and stability of these structures, showing that they can evolve with small amplitude perturbations under certain conditions, while breathers cannot. These findings suggest potential feasibility for experimental observation of these structures.
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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