Discrete spectral symmetries of lowdimensional differential operators and difference operators on regular lattices and twodimensional manifolds
Abstract
EulerDarbouxBacklund and Laplace transformations are considered for the one and twodimensional Schrodinger operators. Their discrete analogs are constructed and generalized for the multidimensional lattices and twomanifolds with special "blackwhite" 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2000
 DOI:
 10.48550/arXiv.mathph/0003009
 arXiv:
 arXiv:mathph/0003009
 Bibcode:
 2000math.ph...3009N
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 LaTeX, 66 pages