  We investigate the frictional sliding of an incommensurate chain of
interacting particles confined in between two nonlinear on-site substrate
potential profiles in relative motion. We focus here on the class of
Remoissenet-Peyrard parametrized potentials $V_{\rm RP}(x,s)$, whose shape can
be varied continuously as a function of $s$, recovering the sine-Gordon
potential as particular case. The observed frictional dynamics of the system,
crucially dependent on the mutual ratios of the three periodicities in the
sandwich geometry, turns out to be significantly influenced also by the shape
of the substrate potential. Specifically, variations of the shape parameter $s$
affects significantly and not trivially the existence and robustness of the
recently reported velocity quantization phenomena [Vanossi {\it et al.}, Phys.
Rev. Lett. 97, 056101 (2006)], where the chain center-of-mass velocity to the
externally imposed relative velocity of the sliders stays pinned to exact
"plateau" values for wide ranges of the dynamical parameters.
