Breathing Bright Solitons in a Bose-Einstein Condensate

A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter-wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very small trap aspect ratio or oscillates with a high frequency, the matter-wave preserves its shape nearly like a soliton train in propagation. While the breathing behaviour, which displays the periodic collapse and revival of the matter-wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass center of the matter-wave translates and/or oscillates for different trap aspect ratio and trap frequnces.