The Discrete AKNS-D Hierarchy

TL;DR

This paper introduces the discrete AKNS-D hierarchy, establishing its construction, proving key identities, and developing the associated tau-functions, thereby advancing the understanding of discrete integrable systems.

Contribution

It provides the first detailed construction and proof of bilinear identities for the discrete AKNS-D hierarchy, including tau-function formulation.

Findings

Established the hierarchy construction.

Proved the bilinear identity.

Constructed tau-functions.

Abstract

In this paper, we consider the discrete AKNS-D hierarchy, find the construction of the hierarchy, prove the bilinear identity and give the construction of the $\tau$-functions of this hierarchy.