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Equations of Advanced–Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems

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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.

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  1. Central Economics and Mathematics Institute of the Russian Academy of Science, 117418, Moscow, Russia

    L. A. Beklaryan

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  1. L. A. Beklaryan
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Beklaryan, L.A. Equations of Advanced–Retarded Type and Solutions of Traveling-Wave Type for Infinite-Dimensional Dynamic Systems. Journal of Mathematical Sciences 124, 5098–5109 (2004). https://doi.org/10.1023/B:JOTH.0000047247.93967.3e

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  • DOI: https://doi.org/10.1023/B:JOTH.0000047247.93967.3e

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