Difference analogue of the Treibich-Verdier operator
Abstract
In [1], it was shown that the one-dimensional finite-gap Schrödinger operator can be extended to a second-order difference operator depending on a small parameter and commuting with some difference operator of order $2g+1.$ In this case, if the small parameter tends to zero, then the second-order difference operator becomes a Schrödinger operator. In this paper, we construct such an extension for the finite-gap Treibich-Verdier operator.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Izvestiya Mathematics
- Volume
- 90
- Issue
- 1
- Pages
- 224–237
- Publication date
- 1 January 2026
- Language
- EN