Together with strange attractors and chaos, solitons play a key role in nonlinear science. Solitons are stable, particle-like, nonlinear pulses which result from a critical balance between nonlinearity and dispersion. My theoretical work is concerned with partial differential equations (PDEs) that admit exact soliton solutions. Such PDEs model shallow water waves, nonlinear optical pulses, currents in electrical networks, nerve pulses, waves in the atmosphere, etc.
Powerful symbolic manipulation programs such as Mathematica, Macsyma, Reduce, Maple, and Derive offer virtually unlimited potential to do mathematics on a computer. The symbol-crunching capabilities of these software packages allow me to obtain soliton solutions without having to do the tedious algebra and calculus with pen and paper.
My research is currently focused on designing symbolic programs that test the integrability of certain nonlinear PDEs and calculate their symmetries, conservation laws, and their exact soliton solutions.
From my student days in Belgium, my curiosity was kindled by real-world applications of mathematics; I was happy to see what "all that stuff was finally used for." My doctoral dissertation dealt with the mathematics of acousto-optics: the interaction of ultrasound and laser light. Engineering applications of acousto-optics include radar signal processing, nondestructive testing, optical computing, laser shows, and medical scanners.
I like to be surrounded by a group of graduate students and work together on symbolic programs and industrial math projects. I have currently started working on the theory and applications of wavelets. Recent problems from industry involved the modeling of acousto-optical materials, the design of speakers, and the positioning of equipment in an open-pit coal mine.
2/8/2005