EXACT BRIGHT SELF-SIMILAR SOLITARY WAVES IN AN EXPULSIVE PARABOLIC POTENTIAL

Exact bright self-similar solitary waves are analytically derived in a cigar-shaped condensate with time-dependent atomic scattering length a(s)(t) in an expulsive parabolic potential. The straightforward relation between the Gross-Pitaevskii equation and the standard nonlinear Schrodinger equation is presented for a(s)(t) = a(0) exp(gamma t) at the growing or decaying coefficient gamma = +/-vertical bar omega(z)vertical bar/omega(t) with omega(z)(omega perpendicular to) the axial (transverse) frequency. In the expulsive parabolic potential, in particular, it is found that the bright self-similar solitary wave is accelerated and set into motion due to the expulsive force. The results tally with the experimental observations by Khaykovich et al. [Science 296 (2002) 1290].