  Complex, localized stable solitons, characterized by a power law behaviour,
are found for a quasi-one-dimensional Bose-Einstein condensate near Feshbach
resonance. Both dark and bright solitons can be excited in the experimentally
allowed parameter domain, when two and three-body interactions are respectively
repulsive and attractive. These solutions are obtained for non-zero chemical
potential, unlike their unstable real counterparts which exist in the limit of
vanishing $\mu$. The dark solitons travel with constant speed, which is quite
different from the Lieb mode, where profiles with different speeds, bounded
above by sound velocity can exist for specified interaction strengths.
