Volterra chain and Catalan numbers

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.

4 pages, 2 figures

Cited by in corpus (2)

• Some exact solutions of the Volterra lattice
• Bogoyavlensky lattices and generalized Catalan numbers