Propagation and breathing of matter–wave-packet trains

We find a set of different orthonormalized states of a nonstationary harmonic oscillator and use them to expand the solution of the Gross-Pitaevskii equation with harmonic potential. The expansion series describes wave-packet trains of a Bose-Einstein condensate, which may be induced initially by the modulational instability. The center of any wave-packet train oscillates like a classical harmonic oscillator of frequency ω. The width and height of the wave packet and the distance between two wave packets change simultaneously like an array of breathers with frequency 2ω. We demonstrate analytically and numerically that for a set of suitable parameters the wave-packet trains can be more exactly fitted to the matter-wave soliton trains observed by Strecker et al. Nature (London) 417 150 (2002)