  We investigate the low-lying excitations of a stack of weakly-coupled
two-dimensional Bose-Einstein condensates that is formed by a one-dimensional
optical lattice. In particular, we calculate the dispersion relations of the
monopole and quadrupole modes, both for the ground state as well as for the
case in which the system contains a vortex along the direction of the lasers
creating the optical lattice. Our variational approach enables us to determine
analytically the dispersion relations for an arbitrary number of atoms in every
two-dimensional condensate and for an arbitrary momentum. We also discuss the
feasibility of experimentally observing our results.
