  We numerically investigated how the nonlinear dynamics depends on the
dimensionality and on the higher-order curvature corrections in the form of
Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances
of a singularity (or black hole) in two models: (i) a perturbed wormhole throat
in spherically symmetric space-time, and (ii) colliding scalar pulses in
plane-symmetric space-time. We used a dual-null formulation for evolving the
field equations, which enables us to locate the trapping horizons directly, and
also enables us to follow close to the large-curvature region due to its causal
integrating scheme. We observed that the fate of a perturbed wormhole is either
a black hole or an expanding throat depending on the total energy of the
structure, and its threshold depends on the coupling constant of the GB terms
($\alpha_{\rm GB}$). We also observed that a collision of large scalar pulses
will produce a large-curvature region, of which the magnitude also depends on
$\alpha_{\rm GB}$. For both models, the normal corrections ($\alpha_{\rm
GB}>0$) work for avoiding the appearance of singularity, although it is
inevitable. We also found that in the critical situation for forming a black
hole, the existence of the trapped region in the Einstein-GB gravity does not
directly indicate the formation of a black hole.
