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 Mat. Zametki, 1997, Volume 62, Issue 4, Pages 588–602 (Mi mz1641)

Completely integrable nonlinear dynamical systems of the Langmuir chains type

V. N. Sorokin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The solution of the Cauchy problem for semi-infinite chains of ordinary differential equations, studied first by O. I. Bogoyavlenskii in 1987, is obtained in terms of the decomposition in a multidimensional continuous fraction of Markov vector functions (the resolvent functions) related to the chain of a nonsymmetric operator; the decomposition is performed by the Euler–Jacobi–Perron algorithm. The inverse spectral problem method, based on Lax pairs, on the theory of joint Hermite–Padé approximations, and on the Sturm–Liouville method for finite difference equations is used.

DOI: https://doi.org/10.4213/mzm1641

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English version:
Mathematical Notes, 1997, 62:4, 488–500

Bibliographic databases:

UDC: 517.53

Citation: V. N. Sorokin, “Completely integrable nonlinear dynamical systems of the Langmuir chains type”, Mat. Zametki, 62:4 (1997), 588–602; Math. Notes, 62:4 (1997), 488–500

Citation in format AMSBIB
\Bibitem{Sor97} \by V.~N.~Sorokin \paper Completely integrable nonlinear dynamical systems of the Langmuir chains type \jour Mat. Zametki \yr 1997 \vol 62 \issue 4 \pages 588--602 \mathnet{http://mi.mathnet.ru/mz1641} \crossref{https://doi.org/10.4213/mzm1641} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620166} \zmath{https://zbmath.org/?q=an:0929.34023} \transl \jour Math. Notes \yr 1997 \vol 62 \issue 4 \pages 488--500 \crossref{https://doi.org/10.1007/BF02358982} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000072500900029} 

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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. Sorokin, V, “Matrix Hermite-Pade problem and dynamical systems”, Journal of Computational and Applied Mathematics, 122:1–2 (2000), 275
2. Aptekarev, A, “The genetic sums' representation for the moments of a system of Stieltjes functions and its application”, Constructive Approximation, 16:4 (2000), 487
3. Smirnova, MC, “Convergence conditions for vector Stieltjes continued fractions”, Journal of Approximation Theory, 115:1 (2002), 100
4. Van Iseghem, J, “Stieltjes continued fraction and QD algorithm: scalar, vector, and matrix cases”, Linear Algebra and Its Applications, 384 (2004), 21
5. Aptekarev, AI, “Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials”, Constructive Approximation, 30:2 (2009), 175
6. Rolania, DB, “Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials”, Journal of Mathematical Analysis and Applications, 361:2 (2010), 358
7. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.
8. Aptekarev A.I., “The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations”, Modern Trends in Constructive Function Theory, Contemporary Mathematics, 661, eds. Hardin D., Lubinsky D., Simanek B., Amer Mathematical Soc, 2016, 167+
9. V. N. Sorokin, “Slabaya asimptotika sovmestnykh mnogochlenov Polacheka”, Preprinty IPM im. M. V. Keldysha, 2017, 026, 20 pp.
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