  In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang
equation in (1+1) dimensions is studied by means of numerical simulations,
focussing on the two-times evolution of an interface in the absence of any
disordered environment. This work shows that even in this simple case, a rich
aging behavior develops. A multiplicative aging scenario for the two-times
roughness of the system is observed, characterized by the same growth exponent
as in the stationary regime. The analysis permits the identification of the
relevant growing correlation length, accounting for the important scaling
variables in the system. The distribution function of the two-times roughness
is also computed and described in terms of a generalized scaling relation.
These results give good insight into the glassy dynamics of the important case
of a non-linear elastic line in a disordered medium.
