Nonlinear Wave Limits of Reversible Finite-State Cellular Automata
We construct reversible finite-state cellular automata whose integer lifts approximate smooth solutions of one-dimensional semilinear wave equations. The kick–drift update is bijective for every odd modulus. Separate rounding of spatial edge contributions and local nonlinear forces gives an exact one-cell support bound for the full local operator algebra. Under a strict Courant condition, a discrete energy estimate bounds the field and staggered-velocity errors by $C_T(h^2+\tau^2+\delta/\tau^2)$ on a fixed physical time interval, where $h$, $\tau$, and $\delta$ are the spatial, temporal, and…
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