We calculate the contained and upward muon and shower fluxes due to neutrinos
produced via dark matter annihilation or decay in the Galactic center. We
consider dark matter models in which the dark matter particle is a gravitino, a
Kaluza-Klein particle and a particle in leptophilic models. The
Navarro-Frenk-White profile for the dark matter density distribution in the
Galaxy is used. We incorporate neutrino oscillations by assuming maximal mixing
and parametrize our results for muon and shower distributions. The muon and
shower event rates and the minimum observation times in order to reach
2$\sigma$ detection significance are evaluated. We illustrate how observation
times vary with the cone half angle chosen about the Galactic center, with the
result that the optimum angles are about 10$^\circ$ and 50$^\circ$ for the muon
events and shower events, respectively. We find that for the annihilating dark
matter models such as the leptophilic and Kaluza-Klein models, upward and
contained muon as well as showers are promising signals for dark matter
detection in just a few years of observation, whereas for decaying dark matter
models, the same observation times can only be reached with showers. We also
illustrate for each model the parameter space probed with the 2$\sigma$ signal
detection in five years. We discuss how the shape of the parameter space probed
change with significance and the observation time.Comment: 19 pages, 20 figures, 9 tables. v2: summary table added, minor typos
corrected, version accepted for publication in Phys. Rev.