14 citations · 77 across the 20 of their papers we have counts for
5 papers · 1 filter
Restrictions on the existence of a canonical system flow hierarchy
Injo Hur, Darren C. Ong
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 nevertheles…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
Wencai Liu, Darren C. Ong
We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
Wencai Liu, Darren C. Ong
In this paper, we consider the Schrödinger equation, \begin{equation*} Hu=-u^{\prime\prime}+(V(x)+V_0(x))u=Eu, \end{equation*} where is 1-periodic and is a decayin…
On a description of the Toda hierarchy using cocycle maps
Darren C. Ong
The Toda hierarchy refers to a family of integrable flows on Jacobi operators that have many applications in mathematics and physics. We demonstrate carefully that an alternative c…
Generalized Toda flows
Darren C. Ong, Christian Remling
The classical hierarchy of Toda flows can be thought of as an action of the (abelian) group of polynomials on Jacobi matrices. We present a generalization of this to the larger gro…