Eur. Phys. J. D (2014) 68: 282
https://doi.org/10.1140/epjd/e2014-50278-0

Regular Article

Rogue matter waves in a Bose-Einstein condensate with the external potential

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China

^a e-mail: tian_bupt@163.com

Received: 3 April 2014
Received in final form: 4 July 2014
Published online: 2 October 2014

Abstract

With the effects of time-dependent external potential, we investigate the rogue matter waves in a Bose-Einstein condensate (BEC), which can be described by the quasi-one-dimensional Gross-Pitaevskii (GP) equation. Darboux transformation (DT) with the multi-parameters for the spectral problem is constructed with the help of gauge transformation. Through a generalized DT, the first- and second-order rogue-wave solutions of the GP equation are obtained. Influence of the linear and harmonic potentials on the background density, peak height and width of the rogue wave is discussed. With the presence of the harmonic potential, rogue wave on the periodic and monotonically increasing background is shown, and its peak height and width can be manipulated. With the presence of the linear potential, the background density of the rogue wave is a constant, and peak height and width of the rogue wave keep invariant. Graphic analysis demonstrates that the oscillating behavior and parabolic trajectory of the rogue wave appear in a BEC with the linear potential.