Fronts and localized solutions in differential equations 

This project would look at the computation and analysis of localized
solutions and propagating fronts. These types are often physically
relevent solutions to differential equations as they determine the
spread of information. A typical example is the FitzHugh-Nagumo
equation which describes neural activity in nerve axons. There are a
number of avenues that can be followed : developing and
analysing efficient computational methods in 2 dimensions; studying
the effect of noise on the stability and computation of waves and 
improving the current models of neural behaviour. The project would
suit someone with an interest in dynamical systems and computational
mathematics. By the end of the PhD you would have a good mix of
practical computational and analytic skills offering a route either
into further research or a position in engineering/high-tech/finacial
industry.