Burchnall-Chaundy Theory
Spectral Theory
2020-01-14 v1 Algebraic Geometry
Abstract
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 of ordinary differential operators. We solve the inverse problem for such data, i.e. we prove that the algebra is (essentially) uniquely determined by its spectral data. The isomorphy type of is uniquely determined by the underlying spectral curve.
Keywords
Cite
@article{arxiv.2001.04266,
title = {Burchnall-Chaundy Theory},
author = {Sebastian Klein and Eva Lübcke and Martin Ulrich Schmidt and Tobias Simon},
journal= {arXiv preprint arXiv:2001.04266},
year = {2020}
}