Mathematical Notes

, Volume 62, Issue 4, pp 488–500 | Cite as

Completely integrable nonlinear dynamical systems of the Langmuir chains type

  • V. N. Sorokin


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.

Key words

nonlinear dynamical system Langmuir chain moments problem multidimensional continuous fraction 


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. N. Sorokin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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