  Phase mixing of relativistic large amplitude nonlinear plasma wave in
presence of a time independent space periodic ion density profile has been
investigated. Inhomogeneous ion along with the relativistic variation of
electron mass make the characteristic frequency of the wave to acquire a space
dependency and thereby it breaks at arbitrarily small amplitude due to phase
mixing. An approximate space time dependent solution is obtained in the weakly
relativistic limit by Bogoliuboff and Kryloff method of averaging. We find that
the change in the ion density perturbation and also the relativistic electron
mass variation have significant effect in modifying the time at which phase
mixing occurs.
