The propagation of solitary waves in clouds of Bose--Einstein condensed atoms

The Gross--Pitaevskii equation which describes the motion of a Bose--Einsteincondensed (BEC) atom in an elongated trap is solved analytically, and a solitary-wave solutionis obtained in the low-density case without neglecting the effect of the interatomicinteraction on the transverse function. It is shown that this effect leads tothe velocity of the solitary wave slowing down and the profileof the solitary wave widening.