Abstract
For a one-dimensional nonautonomous Gross–Pitaevskii system with biperiodically driven interatom interaction and external parabolic potential which satisfy the compatibility conditions (Serkin et al 2007 Phys. Rev. Lett. 98 074102), we derive a set of exact deformed-soliton solutions with amplitudes deviated from the standard hyperbolic-secant form, which describes different single-soliton characteristics of an attractive Bose–Einstein condensate. By defining a deformation factor adjusted by the number of condensed atoms, we find that the analytical height, width, position and velocity of the deformed soliton are controlled by the deformation factor. It is numerically shown that for asymmetric sawtooth driving the temporal ratchet effect can be induced or suppressed, even reversed, by adjusting the factor. The results offer a means of experimentally manipulating directed transports of the nonautonomous solitons.
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