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.
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Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 588–602, October, 1997.
Translated by A. M. Chebotarev
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Sorokin, V.N. Completely integrable nonlinear dynamical systems of the Langmuir chains type. Math Notes 62, 488–500 (1997). https://doi.org/10.1007/BF02358982
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DOI: https://doi.org/10.1007/BF02358982