Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds

摘要

Euler-Darboux-Backlund and Laplace transformations are considered for theone- and two-dimensional Schrodinger operators. Their discrete analogs areconstructed and generalized for the multidimensional lattices and two-manifoldswith special "black-white" triangulations. Nonstandard generalizations of theconnections and curvature are constructed for the simplicial complexes. Exactlysolvable 2D Schrodinger operators with nonstandard spectral properties areconstructed in the continuous and discrete cases using Laplace chains withdifferent restrictions.