We present a general procedure to associate hierarchies of cellular automata with given spectral problems choosing, as illustrative example, the discrete Schrodinger problem. For these cellular automata we construct a countable number of constants of motion using standard spectral techniques and we perform numerical experiments showing interesting dynamical features and particle content. In the second part of the paper we introduce other cellular automata characterized by a very rich particle content and by the existence of constants of motion.
Bruschi, M., Santini, P.m., Ragnisco, O. (1992). INTEGRABLE CELLULAR AUTOMATA. PHYSICS LETTERS A, 169(3), 151-160 [10.1016/0375-9601(92)90585-A].