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

This article is cited in 9 scientific papers (total in 9 papers)

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
Received: 23.04.1996

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
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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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Smirnova, MC, “Convergence conditions for vector Stieltjes continued fractions”, Journal of Approximation Theory, 115:1 (2002), 100  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Van Iseghem, J, “Stieltjes continued fraction and QD algorithm: scalar, vector, and matrix cases”, Linear Algebra and Its Applications, 384 (2004), 21  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Aptekarev, AI, “Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials”, Constructive Approximation, 30:2 (2009), 175  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Rolania, DB, “Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials”, Journal of Mathematical Analysis and Applications, 361:2 (2010), 358  crossref  mathscinet  zmath  isi  scopus  scopus
    7. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    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+  crossref  mathscinet  zmath  isi
    9. V. N. Sorokin, “Slabaya asimptotika sovmestnykh mnogochlenov Polacheka”, Preprinty IPM im. M. V. Keldysha, 2017, 026, 20 pp.  mathnet  crossref
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