Nonlinear waves; integrable systems.
My research involves differential equations that model the propagation of waves in nonlinear dispersive media. In particular, I am interested in the class of exactly solvable wave models known as integrable systems. Integrable systems arise in a wide range of concrete physical applications, from water waves to optical fibers. They possess many rich mathematical properties and are known to admit soliton solutions — localized pulses that propagate without changing their shape or speed. Much of the work I have been involved in deals with mathematically characterizing solitons and other coherent structures using various analytical techniques, as well as studying how they change under the influence of physically relevant non-integrable effects.
Monday/Wednesday 2:00-3:00pm
