English

Volterra chain and Catalan numbers

Exactly Solvable and Integrable Systems 2019-03-29 v1 Combinatorics

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 Catalan numbers.

Cite

@article{arxiv.1810.13198,
  title  = {Volterra chain and Catalan numbers},
  author = {V. E. Adler and A. B. Shabat},
  journal= {arXiv preprint arXiv:1810.13198},
  year   = {2019}
}

Comments

4 pages, 2 figures

R2 v1 2026-06-23T04:58:52.288Z