Restrictions on the existence of a canonical system flow hierarchy
Spectral Theory
2020-10-19 v2
Abstract
The KdV hierarchy is a family of evolutions on a Schr\"odinger operator that preserves its spectrum. Canonical systems are a generalization of Schr\"odinger operators, that nevertheless share many features with Schr\"odinger operators. Since this is a very natural generalization, one would expect that it would also be straightforward to build a hierarchy of isospectral evolutions on canonical systems analogous to the KdV hierarchy. Surprisingly, we show that there are many obstructions to constructing a hierarchy of flows on canonical systems that obeys the standard assumptions of the KdV hierarchy. This suggests that we need a more sophisticated approach to develop such a hierarchy, if it is indeed possible to do so.
Cite
@article{arxiv.1811.11366,
title = {Restrictions on the existence of a canonical system flow hierarchy},
author = {Injo Hur and Darren C. Ong},
journal= {arXiv preprint arXiv:1811.11366},
year = {2020}
}