  Galaxy surveys are an important probe for superimposed oscillations on the
primordial power spectrum of curvature perturbations, which are predicted in
several theoretical models of inflation and its alternatives. In order to
exploit the full cosmological information in galaxy surveys it is necessary to
study the matter power spectrum to fully non-linear scales. We therefore study
the non-linear clustering in models with superimposed linear and logarithmic
oscillations to the primordial power spectrum by running high-resolution
dark-matter-only N-body simulations. We fit a Gaussian envelope for the
non-linear damping of superimposed oscillations in the matter power spectrum to
the results of the N-body simulations for $k \lesssim 0.6\ h/$Mpc at $0 \leq z
\leq 5$ with an accuracy below the percent. We finally use this fitting formula
to forecast the capabilities of future galaxy surveys, such as Euclid and
Subaru, to probe primordial oscillation down to non-linear scales alone and in
combination with the information contained in CMB anisotropies.
