A Discrete Analogue of the Dirac Operator and the Discrete Modified Novikov-Veselov Hierarchy

作者:Zakharov Dmitry*
来源:International Mathematics Research Notices, 2010, (18): 3463-3488.
DOI:10.1093/imrn/rnq014

摘要

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.

  • 出版日期2010