Volterra Chain and Catalan Numbers

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 t...

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Bibliographic Details
Published in:JETP letters 2018-12, Vol.108 (12), p.825-828
Main Authors: Adler, V. E., Shabat, A. B.
Format: Article
Language:English
Subjects:
Atomic
Bessel functions
Biological and Medical Physics
Biophysics
Cauchy problems
Chains
Methods of Theoretical Physics
Molecular
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Quantum Information Technology
Solid State Physics
Spintronics
Taylor series
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Summary: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.
ISSN:0021-3640
1090-6487
DOI:10.1134/S0021364018240013