A discrete analogue of the modified Novikov-Veselov hierarchy

TL;DR

This paper develops a discrete version of the modified Novikov-Veselov hierarchy, including spectral analysis and explicit eigenfunction formulas, advancing the understanding of integrable systems in discrete settings.

Contribution

It introduces a novel discrete analogue of the hierarchy and provides explicit spectral and eigenfunction formulas, expanding integrable systems theory.

Findings

Constructed a discrete integrable Dirac operator.

Derived the first two hierarchy equations.

Provided explicit theta-function eigenfunction formulas.

Abstract

We construct a discrete analogue of the integrable two-dimensional Dirac operator and describe the spectral properties of its eigenfunctions. We construct an integrable discrete analogue of the modified Novikov-Veselov hierarchy. We derive the first two equations of the hierarchy and give explicit formulas for the eigenfunctions in terms of the theta-functions of the associated spectral curve.