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arXiv · 1811.11366

Restrictions on the existence of a canonical system flow hierarchy

Injo Hur·Darren C. Ong
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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.

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Injo Hur, Darren C. Ong. 2018-11-28. Restrictions on the existence of a canonical system flow hierarchy. https://arxiv.org/abs/1811.11366

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