Interaction of Simple Particles in Soliton Cellular Automata
ATHANASSIOS S. FOKAS, Evanthia Papadopoulou, Yiannis G. Saridakis, Mark J. Ablowitz · Studies in Applied Mathematics · 1989
We consider a certain cellular automaton recently introduced by Park, Steiglitz, and Thurston. By introducing appropriate mathematical notation, the interaction of simple particles evolving according to this automaton rule is completely characterized analytically. It is found that: (1) If two particles have different speed and they interact, then they interact solitonically and, although they may interact a number of times, they finally separate with the faster particle moving in front of the slower one. (2) If two particles have the same speed and are close enough so that they interact, there exist two cases: either they will interact only once and then they will separate, travelling independently of each other, or they will form a new periodic configuration by interacting forever.