Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

TL;DR

This paper introduces a non-isospectral extension of the Volterra lattice hierarchy and demonstrates how Hankel determinants derived from Riccati systems provide a complete linearization of these equations.

Contribution

It presents the first Riccati systems for the non-isospectral Volterra hierarchy and shows how Hankel determinants solve these equations, extending the integrability framework.

Findings

Riccati systems for non-isospectral Volterra equations derived

Hankel determinants provide explicit solutions

Complete linearization of the extended hierarchy achieved

Abstract

For the first two equations of the Volterra lattice hierarchy and the first two equations of its non-autonomous (non-isospectral) extension, we present Riccati systems for functions c_j(t), j=0,1,..., such that an expression in terms of Hankel determinants built from them solves these equations on the right half of the lattice. This actually achieves a complete linearization of these equations of the extended Volterra lattice hierarchy.