  We study the vortex dynamics and vortex pinning effect in Bose-Einstein
condensate in a rotating double-well trap potential and co-rotating optical
lattice. We show that, in agreement with the experiment, the vortex number do
not diverge when the rotational frequency $\Omega \rightarrow 1$ if the trap
potential is of anisotropic double-well type. The critical rotational frequency
as obtained from numerical simulations agrees very well with the value $\sqrt
l/l$ for $l=4$ which supports the conjecture that surface modes with angular
momentum $l=4$ are excited when the rotating condensate is trapped in
double-well potential. The vortex lattice structure in a rotating triple-well
trap potential and its pinning shows very interesting features. We show the
existence and pinning of a new type of hidden vortices whose phase profile is
similar to that of the visible vortices.
