Abstract:
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.
Citation:
L. A. Beklaryan, “Equations of Advanced–Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems”, 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, CMFD, 1, MAI, M., 2003, 18–29; Journal of Mathematical Sciences, 124:4 (2004), 5098–5109
\Bibitem{Bek03}
\by L.~A.~Beklaryan
\paper Equations of Advanced--Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems
\inbook 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
\serial CMFD
\yr 2003
\vol 1
\pages 18--29
\publ MAI
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd28}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2129125}
\zmath{https://zbmath.org/?q=an:1069.37062}
\transl
\jour Journal of Mathematical Sciences
\yr 2004
\vol 124
\issue 4
\pages 5098--5109
\crossref{https://doi.org/10.1023/B:JOTH.0000047247.93967.3e}
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