Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
Euler-Darboux-Backlund and Laplace transformations are considered for the one- and two-dimensional Schrodinger operators. Their discrete analogs are constructed and generalized for the multidimensional lattices and two-manifolds with special "black-white" triangulations. Nonstandard generalizations of the connections and curvature are constructed for the simplicial complexes. Exactly solvable 2D Schrodinger operators with nonstandard spectral properties are constructed in the continuous and discrete cases using Laplace chains with different restrictions.
Keywords
Cite
@article{arxiv.math-ph/0003009,
title = {Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds},
author = {S. P. Novikov and I. A. Dynnikov},
journal= {arXiv preprint arXiv:math-ph/0003009},
year = {2007}
}
Comments
LaTeX, 66 pages