  We present four continuations of the critical nonlinear \schro equation (NLS)
beyond the singularity: 1) a sub-threshold power continuation, 2) a
shrinking-hole continuation for ring-type solutions, 3) a vanishing
nonlinear-damping continuation, and 4) a complex Ginzburg-Landau (CGL)
continuation. Using asymptotic analysis, we explicitly calculate the limiting
solutions beyond the singularity. These calculations show that for generic
initial data that leads to a loglog collapse, the sub-threshold power limit is
a Bourgain-Wang solution, both before and after the singularity, and the
vanishing nonlinear-damping and CGL limits are a loglog solution before the
singularity, and have an infinite-velocity{\rev{expanding core}} after the
singularity. Our results suggest that all NLS continuations share the universal
feature that after the singularity time $T_c$, the phase of the singular core
is only determined up to multiplication by $e^{i\theta}$. As a result,
interactions between post-collapse beams (filaments) become chaotic. We also
show that when the continuation model leads to a point singularity and
preserves the NLS invariance under the transformation $t\rightarrow-t$ and
$\psi\rightarrow\psi^\ast$, the singular core of the weak solution is symmetric
with respect to $T_c$. Therefore, the sub-threshold power and
the{\rev{shrinking}}-hole continuations are symmetric with respect to $T_c$,
but continuations which are based on perturbations of the NLS equation are
generically asymmetric.
