2020/01/13 by Sebastian Klein, Klein, Sebastian, Eva Lübcke +6
Mathematics · Physics and Astronomy · #14H70 #47L80 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Spectral Theory (math.SP) #math.AG #math.SP #msc:14H70 #msc:47L80
paper · pdf · doi:10.48550/arxiv.2001.04266
arxiv created 2020/01/13 · openalex publication_date 2020/01/13 · arxiv updated 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Burchnall-Chaundy theory concerns the classification of all pairs of commuting ordinary differential operators. We phrase this theory in the language of spectral data for integrable systems. In particular, we define spectral data for rank 1 commutative algebras A of ordinary differential operators. We solve the inverse problem for such data, i.e. we prove that the algebra A is (essentially) uniquely determined by its spectral data. The isomorphy type of A is uniquely determined by the underlying spectral curve.