  The graphene superlattice equation, a modified sine-Gordon equation, governs
the propagation of solitary electromagnetic waves in a graphene superlattice.
This equation has kink solutions without explicit analytical expression,
requiring the use of quadrature methods. The inelastic collision of kinks and
antikinks with the same but opposite speed is studied numerically for the first
time; after their interaction they escape to infinity when its speed is either
larger than a critical value or it is inside a series of resonance windows;
otherwise, they form a breather-like state that slowly decays by radiating
energy. Here, the fractal structure of these resonance windows is characterized
by using a multi-index notation and their main features are compared with the
predictions of the resonant energy exchange theory showing good agreement. Our
results can be interpreted as new evidence in favour of this theory.
