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The Washington Research Foundation Fellowship
Nate Bottman, Mathematics - 2008-09 WRFF
I entered the UW four years ago through the Early Entrance Program. All I knew about myself was that I loved math more than anything else, so fresh out of the first quarter of Steffen Rohde's brilliant honors calculus class, I started working with Bernard Deconinck. Our goal was to determine the stability properties of some solutions of the nonlinear Schrödinger equation, which is a fundamental equation in mathematical physics, governing the behavior of modulated waves in nonlinear media. The project wasn't without its obstacles --- over the first summer I spent, I was unknowingly replicating some work done in England during the 1970s --- but I kept at it, and the result of our labors is a general method for computing the stability spectra of stationary solutions of integrable equations.
Math has taken me all over the world, including to Moscow, where I spent four months in 2007. There I both fell in love with Russia --- I'm a Russian major now, as well as a math major --- and began working with another of my collaborators, George Shabat, on another project in numerical analysis and elliptic integral theory. I have been able to give a few talks on my work --- one in Atlanta, one in Vancouver, B.C., and too many to count at the UW, through the nonlinear waves research group --- and the hospitality and inclusiveness of the worldwide math community has always amazed me. Thanks in part to the Washington Research Foundation, I don't plan on stopping working on unsolved math problems anytime soon.In my spare time, I enjoy doing math, watching Russian films, baking bread, and drinking coffee.
Mentor: Bernard Deconinck, Applied Mathematics
Project Title: Analytically Determining the Spectra of Stationary Solutions of Integrable Equations
Abstract: Recent years have seen a lot of activity around the stability analysis of stationary