Abstract
We derive exact solitonic solutions of a class of Gross-Pitaevskii equations with time-dependent harmonic trapping potential and interatomic interaction. We find families of exact single-solitonic, multi-solitonic, and solitary wave solutions. We show that, with the special case of an oscillating trapping potential and interatomic interaction, a soliton can be localized indefinitely at an arbitrary position. The localization is shown to be experimentally possible for sufficiently long time even with only an oscillating trapping potential and a constant interatomic interaction.
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