Complex solitons with power law behaviour in Bose-Einstein condensates near Feshbach resonance

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.