  We consider the Cauchy problem for the nonlinear Schr\"odinger equation on
the whole space. After introducing a weaker concept of finite speed of
propagation, we show that the concatenation of initial data gives rise to
solutions whose time of existence increases as one translates one of the
initial data. Moreover, we show that, given global decaying solutions with
initial data $u_0, v_0$, if $|y|$ is large, then the concatenated initial data
$u_0+v_0(\cdot -y)$ gives rise to globally decaying solutions.
