Figure 4

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 c(f2 - 1)2 scalar field potential. The top image (a) shows the 2-bounce windows in dark with the rightmost region ( v/c > 0.25 ) representing the single-bounce regime above which no captured state exists, and the leftmost white region ( v/c < 0.19 ) 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 n -bounce windows is observed at all scales investigated numerically.