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One-dimensional (1D) Nonlinear Schroedinger Equaation (NLS) provides a goodapproximation to attractive Bose-Einshtein condensate (BEC) in a quasi 1Dcigar-shaped optical trap in certain regimes. 1D NLS is an integrable equationthat can be solved through the inverse scattering method. Our observation isthat in many cases the parameters of the BEC correspond to the semiclassical(zero dispersion) limit of the focusing NLS. Hence, recent results about thestrong asymptotics of the semiclassical limit solutions can be used to describesome interesting phenomena of the attractive 1D BEC. In general, thesemiclassical limit of the focusing NLS exibits very strong modulationinstability. However, in the case of an analytical initial data, the NLSevolution does displays some ordered structure, that can describe, for example,the bright soliton phenomenon. We discuss some general features of thesemiclassical NLS evolution and propose some new observables.

Temporal evolution of attractive Bose-Einstein condensate in a quasi 1D  cigar-shape trap modeled through the semiclassical limit of the focusing  Nonlinear Schroedinger Equation