Geodesic
Equations of Advanced--Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, Tome 1 (2003), pp. 18-29

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In the paper we study infinite-dimensional dynamic systems with the Frenkel–Kontorova potentials. For such systems we describe their traveling-wave-type solutions, which are solutions for the corresponding boundary-value problem with nonlocal conditions. Describing the mentioned solutions is equivalent to describing the space of solutions for a functional differential equation that can be canonically derived from the original dynamic system. The stability of traveling-wave-type solutions is also investigated. 
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     author = {L. A. Beklaryan},
     title = {Equations of {Advanced--Retarded} {Type} and {Solutions} of {Traveling-Wave} {Type} for {Infinite-Dimensional} {Dynamic} {Systems}},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2003_1_a1/}
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L. A. Beklaryan. Equations of Advanced--Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, Tome 1 (2003), pp. 18-29. http://geodesic.mathdoc.fr/item/CMFD_2003_1_a1/