My current research area concerns mathematical physics and dynamical systems.
I am interested in direct and inverse spectral theory for differential and
difference operators in connection with completely integrable nonlinear wave equations.
In particular, I am studying Schrödinger and Jacobi
operators and their connections with the Korteweg-de Vries and
Toda hierarchies of nonlinear evolution equations.

My research is funded by the Austrian Science Fund (FWF). Further information can be found on the corresponding project pages:

More precisely, my interests can be split up as follows:

- Spectral theory for Schrödinger, Sturm-Liouville, Dirac, and Jacobi operators
- Spectral deformations (Darboux type transformations)
- Inverse spectral theory, trace formulas
- Direct and inverse scattering theory
- Weyl asymptotics
- Measure theory
- Fourier analysis

- Oscillation theory

- Bäcklund transformations
(
*N*-soliton solutions on arbitrary background) - Inverse scattering transform
- Stability/Long time asymptotics (nonlinear steepest descent)

- Applications of the theory of hyperelliptic curves (in particular Jacobi's inversion problem on Riemann surfaces) to completely integrable wave equations
- Hierarchies of completely integrable wave equations (Korteweg-de Vires, Toda, Ablowitz-Ladik)
- Algebro-geometric solutions (quasi periodic solutions)
- Riemann-Hilbert problems on Riemann surfaces

- Abstract wave equations
- Kinetic equations (Vlasov equation coupled to field equations)
- Nonlinear wave equations (Korteweg-de Vries, Camassa-Holm)

- Modeling of the respiratory and cardiovascular system

A complete list of publications (including TeX/PDF versions for downloading) is available.