Geodesic
Discrete Schr\"odinger Equation on a~Finite Field and Associated Cellular Automaton
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 319-330

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The discrete Schrödinger equation with potential belonging to $\mathbb F_2$ is solved explicitly. On this base, the associated $(1+1)$-dimensional cellular automaton is examined and a corresponding set of integrals of motion is constructed. 
@article{TM_1999_225_a20,
     author = {A. K. Pogrebkov},
     title = {Discrete {Schr\"odinger} {Equation} on {a~Finite} {Field} and {Associated} {Cellular} {Automaton}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {319--330},
     publisher = {mathdoc},
     volume = {225},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_225_a20/}
}
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A. K. Pogrebkov. Discrete Schr\"odinger Equation on a~Finite Field and Associated Cellular Automaton. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 319-330. http://geodesic.mathdoc.fr/item/TM_1999_225_a20/