Geodesic
A~dynamical system with infinitely many degrees of freedom and solution of the Frenkel'--Kontorova problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 58-68

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A system with infinitely many particles and Frenkel'–Kontorova potential is studied. Solutions of the Frenkel'–Kontorova problem are found, the stability of the stationary solutions is proved, and families of synchronous, periodic, and conditionally periodic motions are constructed. 
@article{TMF_1986_68_1_a4,
     author = {L. D. Pustyl'nikov},
     title = {A~dynamical system with infinitely many degrees of freedom and solution of the {Frenkel'--Kontorova} problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {58--68},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a4/}
}
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L. D. Pustyl'nikov. A~dynamical system with infinitely many degrees of freedom and solution of the Frenkel'--Kontorova problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 1, pp. 58-68. http://geodesic.mathdoc.fr/item/TMF_1986_68_1_a4/