C. Jordan Allen-Flowers

In broad terms, my research deals with the analysis of nonlinear partial differential equations.  To this end, I use a wide range of tools from applied mathematics, including asymptotic methods and numerical simulation.  I am particularly interested in nonlinear wave theory as it applies to optical sciences.

My current research deals with singularity formation and regularization in the nonlinear Schrodinger equation.  This research is useful for describing a process known as filamentation, where a laser beam can "self-focus" to intensities high enough to ionize the air.  With Dr. Karl Glasner, we are working on an analytical framework for modeling how one of these filaments might interact with an ambient field, with the end goal being able to control filament-filament interactions.

I have also worked on projects with internal gravity waves, flame propagation, nonlinear transmission lines, and fiber optics.