Abstract:
In this paper, it is derived a rich hierarchy for the Toda lattice with a self-consistent source in the class of periodic functions. We discuss the complete integrability of the constructed systems that is based on the transformation to the spectral data of an associated discrete Hill`s equation with periodic coefficients. In particular, Dubrovin-type equations are derived for the time-evolution of the spectral data corresponding to the solutions of any system in the hierarchy. At the end of the paper, we illustrate our theory on concrete example with analytical and numerical results.
Citation:
B. A. Babajanov, M. M. Ruzmetov, “On the construction and integration of a hierarchy for the periodic Toda lattice with a self-consistent source”, Bulletin of Irkutsk State University. Series Mathematics, 38 (2021), 3–18
\Bibitem{BabRuz21}
\by B.~A.~Babajanov, M.~M.~Ruzmetov
\paper On the construction and integration of a hierarchy for the periodic Toda lattice with a self-consistent source
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2021
\vol 38
\pages 3--18
\mathnet{http://mi.mathnet.ru/iigum465}
\crossref{https://doi.org/10.26516/1997-7670.2021.38.3}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000744196900001}
Linking options:
https://www.mathnet.ru/eng/iigum465
https://www.mathnet.ru/eng/iigum/v38/p3
This publication is cited in the following 2 articles:
Bazar Babajanov, Murod Ruzmetov, Sherzod Sadullaev, NOVEL TRENDS IN RHEOLOGY IX, 2997, NOVEL TRENDS IN RHEOLOGY IX, 2023, 020023
B.A. Babajanov, M.M. Ruzmetov, Sh.O. Sadullaev, “Integration of the finite complex Toda lattice with a self-consistent source”, Partial Differential Equations in Applied Mathematics, 7 (2023), 100510
Citation in format AMSBIB
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