  The parametric decay of finite-size Alfv\'en waves in nonperiodic low-beta
plasmas is investigated using one-dimensional hybrid simulations. Compared with
the usual small periodic system, a wave packet in a large system under the
absorption boundary condition shows different decay dynamics, including reduced
energy transfer and localized density cavitation and ion heating. The resulting
Alfv\'en wave dynamics are influenced by several factors of the instability
including the growth rate, central wave frequency, and unstable bandwidth. A
final steady state of the wave packet may be achieved when the instability does
not have enough time to develop within the residual packet, and the packet size
shows well-defined scaling dependencies on the growth rate, wave amplitude, and
plasma beta. Under the proper conditions enhanced secondary decay can also be
excited in the form of a narrow, amplified wavepacket. These results may help
interpret laboratory and spacecraft observations of Alfv\'en waves, and refine
our understanding of associated energy transport and ion heating.
