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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
R. Ch. Kulaev and A. B. Shabat, Ufa Math. J. (2018, accepted).
N. J. A. Sloane, http://oeis.org (2010).
J. W. Layman, J. Integer Seq. 4, 01.1.5 (2001).
Y. Kodama and V. U. Pierce, Comm. Math. Phys. 292, 529 (2009).
A. N. Leznov, Theor. Math. Phys. 42, 225 (1980).
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas (Dover, New York, 1972).
O. I. Bogoyavlensky, Russ. Math. Surv. 46 (3), 1 (1991).
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics (Addison-Wesley, Reading, MA, 1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 108, No. 12, pp. 834–837.
The article is published in the original.
Rights and permissions
About this article
Cite this article
Adler, V.E., Shabat, A.B. Volterra Chain and Catalan Numbers. Jetp Lett. 108, 825–828 (2018). https://doi.org/10.1134/S0021364018240013
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364018240013