2018/11/28 by Hur, Injo, Ong, Darren C.
#FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1811.11366
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.