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Volterra Chain and Catalan Numbers

  • Methods of Theoretical Physics
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Abstract

We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for the Catalan numbers.

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Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Russian Academy of Science, Chernogolovka, Moscow region, 142432, Russia

    V. E. Adler & A. B. Shabat

Authors
  1. V. E. Adler
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  2. A. B. Shabat
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Corresponding author

Correspondence to V. E. Adler.

Additional information

Published in Russian in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 108, No. 12, pp. 834–837.

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Adler, V.E., Shabat, A.B. Volterra Chain and Catalan Numbers. Jetp Lett. 108, 825–828 (2018). https://doi.org/10.1134/S0021364018240013

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  • DOI: https://doi.org/10.1134/S0021364018240013