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.
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