David J. Kaup

Provost Distinguished Research Professor
Department of Mathematics
University of Central Florida
Orlando, FL 32816
Phone: (407) 823-2795
FAX: (407) 823-3499
Email address: kaup@ucf.edu

Research Interests

My research interests are mostly in the area of "nonlinear waves". What is a "nonlinear wave"? Well, have you ever watched waves coming into a beach? Out in the deep water, they are small. As they move in toward shore, they grow and finally break into foam. That is one example of a nonlinear wave. Another is the magnetron in your microwave. A magnetron uses magnetic fields to generate electron waves, which use a nonlinear interaction to produce the microwaves that heat your food. Furthermore, certain types of nonlinear waves (actually pulses), called "solitons", have also been proposed as information bit carriers in optical fibers. So, nonlinear waves are actually very common and very useful.

There are many ways to study nonlinear waves. One can simply study the mathematical theory of these waves, for itself. This area has a very rich and interesting mathematical structure. On the other hand, those systems which do support soliton solutions are particularly fascinating, simply because, although they have a very simple but rich structure, nevertheless they are still sufficiently complex to model many physical phenomena. This in itself is very interesting. Why should such simple systems be able to model so many physical phenomena?

This already brings us into the next reason to study nonlinear waves, and that is for "applications". Many physical phenomena can often be reduced to only one or two, or perhaps three, effects competing against one another. When this can be done, then one has an excellent chance to successfully model this system with mathematics. Invariably this modeling will result in nonlinear waves being present. So if one can understand how nonlinear waves behave, one now can start to work backwards, to an explanation of a physical system.

Above all this, there is the study of "modeling". Real modeling is more than just curve fitting. How does one really model something? Is there a science to this? It is currently more or less an art, but there has to be a technology behind modeling. However the laws and rules of it are still to be detailed and summarized. That is just more work for the future.