Figure 4:
Fractal structure of the transition
between reflected and captured states for
colliding
kink-antikink solitons in the
parameter space of impact velocity for a
scalar field
potential. The top image (a) shows
the 2-bounce windows in dark with the rightmost
region
(
) representing the single-bounce
regime above which no captured state exists, and
the
leftmost white region (
) representing the captured state
below which no reflection windows
exist. Between these two marker
velocities, there are 2-bounce reflection states of
decreasing widths
separated by regions of bion
formation. Zooming in on the domain outlined by the
dashed box, a
self-similar structure is apparent
in the middle image (b), where now the dark regions
represent
3-bounce windows of decreasing
widths. Zooming in once again on the boundaries of these
3-bounce
windows, a similar structure is
found as shown in the bottom image (c) but with 4-bounce
reflection
windows. This pattern of
self-similarity characterized by
-bounce windows is observed at all
scales
investigated numerically.
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