Nonlinear Wave Propagation

The project will focus on the propagation of waves in mathematical models based on nonlinear evolution equations. These models could arise from applications in chemistry, biology or physics. In particular, the aim will be to determine the complete large-time structure of the solution to a range of initial-value and initial boundary-value problems. Of specific interest will be the large-time attractors for the solutions to the problems considered. The nonlinear systems to be examined admit structures that are temporally or spatially coherent, and these coherent structures could be extremely simple (such as an expansion wave solution) or be very complex (being formed from a collection of simpler structures). The project requires the application of a range of mathematical techniques including: the method of matched asymptotic expansions, dynamical systems theory, the theory of ordinary and partial differential equations and numerical methods. Training will be provided the in above areas, but experience in the theory of differential equations is a prerequisite.