Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

TL;DR

This paper explores the hungry Volterra hierarchy's connection to the multi boson KP hierarchy, introduces fractional Bäcklund transformations, and investigates their relation to two matrix models and the 2D Toda lattice reduction.

Contribution

It constructs fractional Bäcklund transformations for the hungry Volterra hierarchy and links the discrete hungry Volterra equation to two matrix models and the 2D Toda lattice.

Findings

Fractional Bäcklund transformations are developed for the hungry Volterra hierarchy.

The relation between the hungry Volterra equation and two matrix models is established.

Reduction from discrete 2D Toda lattice to hungry Volterra equation is analyzed.

Abstract

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the B\"{a}cklund transformations (BT) which are not the ordinary ones. We call them ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.