  The dynamics of weakly interacting three-dimensional Bose-Einstein
condensates (BECs), trapped in external axially symmetric plus anharmonic
distortion potential are studied. Within a variational approach and
time-dependent Gross-Pitaevskii equation, the coupled condensate width
equations are derived. By modulating anharmonic distortion of the trapping
potential, nonlinear features are studied numerically and illustrated
analytically, such as mode coupling of oscillation modes, and resonances.
Furthermore, the stability of attractive interaction BEC in both repulsive and
attractive anharmonic distortion is examined. We demonstrate that a small
repulsive and attractive anharmonic distortion is effective in reducing
(extending) the condensate stability region since it decreases (increases) the
critical number of atoms in the trapping potential.
