Some Exact Solutions of the Volterra Lattice
Abstract
We study solutions of the Volterra lattice satisfying the stationary equation for its nonautonomous symmetry. We show that the dynamics in t and n are governed by the respective continuous and discrete Painlevé equations and describe the class of initial data leading to regular solutions. For the lattice on the halfaxis, we express these solutions in terms of the confluent hypergeometric function. We compute the Hankel transform of the coefficients of the corresponding Taylor series based on the Wronskian representation of the solution.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 October 2019
 DOI:
 10.1134/S0040577919100039
 arXiv:
 arXiv:1903.11901
 Bibcode:
 2019TMP...201.1442A
 Keywords:

 Volterra lattice;
 symmetry;
 Painlevé equation;
 confluent hypergeometric function;
 Hankel transformation;
 Catalan number;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematics  Combinatorics;
 37K10;
 34M55;
 33C15;
 05A10
 EPrint:
 17 pages, 4 figures