SOLITON CELLULAR AUTOMATA

We study the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by Park, Steiglitz and Thurston. Any given state can be thought of as a collection of particles. We find that: (a) The interaction properties of these particles are richer than the usual solitons. In particular periodic particles may interact solitonically or they may recombine to form new periodic configurations. Even if two particles interact solitonically, they may interact several times before they get separated with the faster particle moving to the left of the slower one. (b) Arbitrary initial data will decompose as t→∞ into a number of periodic particles, and into a number of certain new periodic coherent structures which we call breathers. The particles and the breathers are ordered according to their speed. (c) We formulate the above cellular automaton as a difference equation. This formulation implies that the coherent structures found here are a manifestation of the coupling between the linear part and the nonlinear part of the difference equation. © 1990.