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We derive exact solitonic solutions of the one-dimensional time-dependentGross-Pitaevskii equation with time-dependent strengths of the harmonicexternal potential and the interatomic interaction. The time-dependence of theexternal potential and interatomic interaction are given in terms of a generalfunction of time. For an oscillating strength of the external potential, thesolutions correspond to breathing single and multiple solitons. The amplitudeand frequency of the oscillating potential can be used to control the dynamicsof the center of mass of the solitons. For certain values of these parameters,the solitons can be {\it trapped} at the center of the harmonic potential.

Exact Solitonic Solutions of the One-Dimensional Gross-Pitaevskii Equation with a Time-Dependent Harmonic Potential and Interatomic Interaction