Abstract
It is found that localized solitons in the strongly coupled cigar shaped Bose-Einstein condensate form two distinct classes. The one without a background is an asymptotically vanishing, localized soliton, having a wave-number, which has a lower bound in magnitude. Periodic soliton trains exist only in the presence of a background, where the localized soliton has a \textit{W}-type density profile. This soliton is well suited for trapping of neutral atoms and is found to be stable under Vakhitov-Kolokolov criterion, as well as numerical evolution. We identify an insulating phase of this system in the presence of an optical lattice. It is demonstrated that the -type density profile can be precisely controlled through trap dynamics.
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