Fractal Structures in Multi-soliton Collisions

The breather collisions in a weakly discrete sine-Gordon (SG) equation, revealing a mechanism of fractal soliton scattering, was analyzed. The breather-breather (BB) interactions in the discrete Frenkel-Kontorova (FK) system were compared with the exact BB solution of the unperturbed SG equation. The break-up of the BB system into two separate breathers was studied as a function of the initial distance between the breathers. It was found that the breathers attract each other with a weak force in a weakly discrete SG system