  We present here a detailed numerical study of the dynamical behaviour of
`soft' uncompressed grains in a granular chain where the grains interact via
the intrinsically nonlinear Hertz force. It is well known that such a chain
supports the formation of solitary waves (SWs). Here, however, the system
response to the material properties of the grains and boundaries is further
explored. In particular, we examine the details of the transition of the system
from a SW phase to an equilibrium-like (or quasi-equilibrium) phase and for
this reason we ignore the effects of dissipation in this study. We find that
the soft walls slow the reflection of SWs at the boundaries of the system,
which in turn slows the journey to quasi-equilibrium. Moreover, the increased
grain-wall compression as the boundaries are softened results in fewer average
grain-grain contacts at any given time in the quasi-equilibrium phase. These
effects lead to increased kinetic energy fluctuations in the short term in
softer systems. We conclude with a toy model which exploits the results of
soft-wall systems. This toy model supports the formation of breather-like
entities and may therefore be useful for localizing energy in desired places in
the granular chain.
