  We study decay properties for solutions to the initial value problem
associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We
prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$,
centered on some characteristic curves coming from the underlying transport
equations associated with the ZR/BR system. Additionally, we prove decay to
zero of the local energy-norm in so-called far-field regions. Our results are
independent of the size of the initial data and do not require any parity
condition.
