Martin Klaus

Broadly speaking, my research area is the spectral theory and inverse scattering theory of linear operators and nonlinear evolution equations arising in mathematical physics.

Over the past few years, my focus of research has been the spectrum of certain linear systems of differential equations (the Zakharov-Shabat and AKNS systems) which play a crucial role in the solution of the nonlinear Schrödinger equation by means of the inverse scattering technique. The nonlinear Schrödinger equation is the partial differential equation that governs the propagation of pulses in optical fibers; it is studied extensively in the mathematical and engineering literature.

The study of the spectrum of these systems poses interesting challenges and progress on the mathematical side may have direct consequences for the design of fiber optic systems.