Abstract:
Cauchy's problem for Toda lattices with initial data equal to the sum of a periodic
and a rapidly decreasing sequence is solved with the use of the inverse scattering method. A method allowing one to find a limit periodic solution of the Toda lattice from a known periodic solution is described. The existence and uniqueness of a limit periodic solution is proved.
Bibliography: 17 titles.
Citation:
A. Kh. Khanmamedov, “The solution of Cauchy's problem for the Toda lattice with limit periodic initial data”, Sb. Math., 199:3 (2008), 449–458
\Bibitem{Kha08}
\by A.~Kh.~Khanmamedov
\paper The solution of Cauchy's problem for the Toda lattice with limit periodic initial data
\jour Sb. Math.
\yr 2008
\vol 199
\issue 3
\pages 449--458
\mathnet{http://mi.mathnet.ru/eng/sm3847}
\crossref{https://doi.org/10.1070/SM2008v199n03ABEH003927}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2409495}
\zmath{https://zbmath.org/?q=an:1161.37051}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000257185400006}
\elib{https://elibrary.ru/item.asp?id=20359315}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-48049123654}
Linking options:
https://www.mathnet.ru/eng/sm3847
https://doi.org/10.1070/SM2008v199n03ABEH003927
https://www.mathnet.ru/eng/sm/v199/i3/p133
This publication is cited in the following 4 articles:
Aleskerov I R., “An Application of the Inverse Scattering Problem For the Discrete Dirac Operator”, Proc. Inst. Math. Mech., 46:1 (2020), 94–101
M. G. Makhmudova, A. Kh. Khanmamedov, “Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice”, Comput. Math. Math. Phys., 55:12 (2015), 2008–2013
Teschl G., “On the spatial asymptotics of solutions of the Toda lattice”, Discrete Contin. Dyn. Syst., 27:3 (2010), 1233–1239
Egorova I., Michor J., Teschl G., “Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds”, J. Math. Phys., 50:10 (2009), 103521, 9 pp.
Citation in format AMSBIB
Contact us: