Difference Krichever-Novikov operators

2014/08/01 by G. S. Mauleshova, Gulnara S. Mauleshova, Mauleshova, Gulnara S. +2
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics #nlin.SI

paper · pdf · doi:10.48550/arxiv.1408.0113

16 pages

arxiv created 2014/08/01 · openalex publication_date 2014/08/01 · arxiv updated 2014/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study commuting difference operators of rank two. We introduce an equation on potentials V(n),W(n) of the difference operator L₄=(T+V(n)T^-1)²+W(n) and some additional data. With the help of this equation we find the first examples of commuting difference operators of rank two corresponding to spectral curves of higher genus.

Citations

• Commutative Ordinary Differential Operators

Related

• Positive one-point commuting difference operators
• Commuting differential and difference operators associated to complex curves, II
• Commuting higher rank ordinary differential operators
• Finite-gap difference opeators with elliptic coefficients and their spectral curves
• Novikov equations for commuting differential operators of orders 3,4,5