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 TMF, 1997, Volume 111, Number 3, Pages 335–344 (Mi tmf1012)

Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data

V. L. Vereshchagin

Irkutsk Computer Centre, Siberian Branch of RAS

Abstract: The connection between a solution of the Volterra chain tending at infinity to constans and the Riemannian curve of genus one modulated in the sence of Witham is described. The leading term of the asymptotic expansion of the solution is constructed.

DOI: https://doi.org/10.4213/tmf1012

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English version:
Theoretical and Mathematical Physics, 1997, 111:3, 658–666

Bibliographic databases:

Citation: V. L. Vereshchagin, “Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data”, TMF, 111:3 (1997), 335–344; Theoret. and Math. Phys., 111:3 (1997), 658–666

Citation in format AMSBIB
\Bibitem{Ver97} \by V.~L.~Vereshchagin \paper Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data \jour TMF \yr 1997 \vol 111 \issue 3 \pages 335--344 \mathnet{http://mi.mathnet.ru/tmf1012} \crossref{https://doi.org/10.4213/tmf1012} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1472212} \zmath{https://zbmath.org/?q=an:0978.35502} \transl \jour Theoret. and Math. Phys. \yr 1997 \vol 111 \issue 3 \pages 658--666 \crossref{https://doi.org/10.1007/BF02634054} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YC44100002} 

• http://mi.mathnet.ru/eng/tmf1012
• https://doi.org/10.4213/tmf1012
• http://mi.mathnet.ru/eng/tmf/v111/i3/p335

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. M. Guseinov, A. Kh. Khanmamedov, “The $t\to\infty$ asymptotic regime of the Cauchy problem solution for the Toda chain with threshold-type initial data”, Theoret. and Math. Phys., 119:3 (1999), 739–749
2. Svinin, AK, “Reductions of the Volterra lattice”, Physics Letters A, 337:3 (2005), 197
3. Khanmamedov A.K., “On the integration of an initial-boundary value problem for the Volterra lattice”, Differential Equations, 41:8 (2005), 1192–1195
4. Khanmamedov, AK, “Initial-boundary value problem for the Volterra lattice on a half-line with zero boundary condition”, Doklady Mathematics, 78:3 (2008), 848
5. A. Kh. Khanmamedov, “The Cauchy problem for a semi-infinite Volterra chain with an asymptotically periodic initial condition”, Siberian Math. J., 51:2 (2010), 346–356
6. 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
7. R. Ch. Kulaev, A. B. Shabat, “Conservation laws for Volterra chain with initial step-like condition”, Ufa Math. J., 11:1 (2019), 63–69
8. Aleskerov I R., “An Application of the Inverse Scattering Problem For the Discrete Dirac Operator”, Proc. Inst. Math. Mech., 46:1 (2020), 94–101
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