  We consider $L^{2}$-supercritical and $H^{1}$-subcritical focusing nonlinear
Schr\"odinger equations. We introduce a subset $PW$ of $H^{1}(\mathbb{R}^{d})$
for $d\ge 1$, and investigate behavior of the solutions with initial data in
this set. For this end, we divide $PW$ into two disjoint components $PW_{+}$
and $PW_{-}$. Then, it turns out that any solution starting from a datum in
$PW_{+}$ behaves asymptotically free, and solution starting from a datum in
$PW_{-}$ blows up or grows up, from which we find that the ground state has two
unstable directions. We also investigate some properties of generic global and
blowup solutions.
