Title: Matter-wave solutions in the Bose-Einstein condensates with the harmonic and Gaussian potentials,
Abstract: We study exact solutions of the quasi-one-dimensional Gross-Pitaevskii (GP)
equation with the (space, time)-modulated potential and nonlinearity and the
time-dependent gain or loss term in Bose-Einstein condensates. In particular,
based on the similarity transformation, we report several families of exact
solutions of the GP equation in the combination of the harmonic and Gaussian
potentials, in which some physically relevant solutions are described. The
stability of the obtained matter-wave solutions is addressed numerically such
that some stable solutions are found. Moreover, we also analyze the parameter
regimes for the stable solutions. These results may raise the possibility of
relative experiments and potential applications.