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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 2, Pages 372–410 (Mi izv1450)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics as $t\to\infty$ of the solution of the Cauchy problem for a two-dimensional generalization of the Toda lattice

V. Yu. Novokshenov


Abstract: The leading term of the asymptotics of a solution of the nonlinear hyperbolic system
$$ \square u_n=\exp(u_{n+1}-u_n)-\exp(u_n-u_{n-1}),\qquad n=1,2,…,N, $$
for large times is constructed and justified. A version of the method of the inverse problem reducing to the solution of a matrix problem of linear conjugation on the complex plane of the spectral parameter is used to solve this system. The coefficients of the asymptotics of $u_n$ are expressed explicitly in terms of the elements of the Riemann matrix realizing the linear conjugation. A theorem is proved on the approximation of the exact solution by the asymptotics constructed.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 24:2, 347–382

Bibliographic databases:

UDC: 517.946
MSC: Primary 35L70, 35B40; Secondary 35Q20
Received: 28.10.1982

Citation: V. Yu. Novokshenov, “Asymptotics as $t\to\infty$ of the solution of the Cauchy problem for a two-dimensional generalization of the Toda lattice”, Izv. Akad. Nauk SSSR Ser. Mat., 48:2 (1984), 372–410; Math. USSR-Izv., 24:2 (1985), 347–382

Citation in format AMSBIB
\Bibitem{Nov84}
\by V.~Yu.~Novokshenov
\paper Asymptotics as $t\to\infty$ of the solution of the Cauchy problem for a~two-dimensional generalization of the Toda lattice
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 2
\pages 372--410
\mathnet{http://mi.mathnet.ru/izv1450}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=740796}
\zmath{https://zbmath.org/?q=an:0566.35091}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 2
\pages 347--382
\crossref{https://doi.org/10.1070/IM1985v024n02ABEH001238}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kitaev, “The method of isomonodromy deformations and the asymptotics of solutions of the “complete” third Painlevé equation”, Math. USSR-Sb., 62:2 (1989), 421–444  mathnet  crossref  mathscinet  zmath
    2. V. V. Sukhanov, “An inverse problem for a selfadjoint differential operator on the line”, Math. USSR-Sb., 65:1 (1990), 249–266  mathnet  crossref  mathscinet  zmath
    3. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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