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Restrictions on the Existence of a Canonical System Flow Hierarchy

Authors
  • Hur, Injo1
  • Ong, Darren C.2
  • 1 Chonnam National University, 77 Yongbong-ro, Buk-gu, Gwangju, 61186, Republic of Korea , Gwangju (South Korea)
  • 2 Xiamen University Malaysia, Jalan Sunsuria, Bandar Sunsuria, Sepang, Selangor, 43900, Malaysia , Sepang (Malaysia)
Type
Published Article
Journal
Integral Equations and Operator Theory
Publisher
Springer International Publishing
Publication Date
Jun 21, 2021
Volume
93
Issue
4
Identifiers
DOI: 10.1007/s00020-021-02647-3
Source
Springer Nature
Keywords
Disciplines
  • Article
License
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Abstract

The KdV hierarchy is a family of evolutions on a Schrödinger operator that preserves its spectrum. Canonical systems are a generalization of Schrödinger operators, that nevertheless share many features with Schrödinger 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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