On the Inverse Resonance Problem for Schrodinger Operators (2009)
Marletta, Marco, Shterenberg, Roman, Weikard, Rudi
We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that...
Gesztesy, Friedrich, Race, David, Weikard, Rudi
We study Bäcklund transformations for a Boussinesq- or nonlinear string-type equation and explicitly construct solutions for the associated modified equations. Our main results involve Miura-type...
A Borg-Levinson theorem for trees (2005)
Brown, Brian Malcolm, Weikard, Rudi
We prove that the Dirichelet-to-Neumann map for a Schrödinger operator on a finite simply connected tree determines uniquely the potential on that tree.
A Borg-Levinson theorem for trees (2005)
Brown, Brian Malcolm, Weikard, Rudi
We prove that the Dirichelet-to-Neumann map for a Schrödinger operator on a finite simply connected tree determines uniquely the potential on that tree.
Marletta, Marco, Weikard, Rudi
It is well known that knowing the Dirichlet–Dirichlet eigenvalues and the Dirichlet–Neumann eigenvalues determines uniquely the potential of a one-dimensional Schrödinger equation on a finite...
Marletta, Marco, Weikard, Rudi
It is well known that knowing the Dirichlet–Dirichlet eigenvalues and the Dirichlet–Neumann eigenvalues determines uniquely the potential of a one-dimensional Schrödinger equation on a finite...
On the inverse resonance problem (2003)
Brown, Brian Malcolm, Knowles, I., Weikard, Rudi
A new technique is presented which gives conditions under which perturbations of certain base potentials are uniquely determined from the location of eigenvalues and resonances in the context of a...
On the inverse resonance problem (2003)
Brown, Brian Malcolm, Knowles, I., Weikard, Rudi
A new technique is presented which gives conditions under which perturbations of certain base potentials are uniquely determined from the location of eigenvalues and resonances in the context of a...
On a Theorem of Halphen and its Application to Integrable Systems (2003)
Gesztesy, Fritz, Unterkofler, Karl, Weikard, Rudi
We extend Halphen's theorem which characterizes the solutions of certain $n$th-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order $n \times...
An Explicit Characterization of Calogero--Moser Systems (2003)
Gesztesy, Fritz, Unterkofler, Karl, Weikard, Rudi
Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly...
Elliptic Algebro-Geometric Solutions of the KdV and AKNS Hierarchies - An Analytic Approach (1998)
Gesztesy, Fritz, Weikard, Rudi
We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our treatment includes an...
A Characterization of All Elliptic Solutions of the AKNS Hierarchy (1997)
Gesztesy, Fritz, Weikard, Rudi
An explicit characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy is presented. Our approach is based on (an extension of) a classical theorem of Picard, which guarantees...