  By direct numerical simulation and variational solution of the
  Gross-Pitaevskii equation, we studied the stationary and dynamic
characteristics of a cigar-shaped, localized, collisionally inhomogeneous
Bose-Einstein condensate trapped in a one-dimensional bichromatic
quasi-periodic optical-lattice potential, as used in a recent experiment on the
localization of a Bose-Einstein condensate
  [Roati et al., Nature (London) {\bf 453}, 895 (2008)]. The effective
potential characterizing the spatially modulated nonlinearity is obtained. It
is found that the collisional inhomogeneity has influence not only on the
central region but also on the tail of the Bose-Einstein condensate. The
influence depends on the sign and value of the spatially modulated nonlinearity
coefficient. We also demonstrate the stability of the stationary localized
stat$ performing a standard linear stability analysis. Where possible, the
numerical results are shown to be in good agreement with the variational
results.
