Some exact solutions of the Volterra lattice

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 half-axis, 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.