A discrete analogue of the dirac operator and the discrete modified Novikov-Veselov hierarchy

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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.

Original languageEnglish
Pages (from-to)3463-3488
Number of pages26
JournalInternational Mathematics Research Notices
Volume2010
Issue number18
DOIs
StatePublished - 2010

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