Potential Supervision Topics:

Nonlinear optics: The propagation of solitary waves and dispersive shock waves in nematic liquid crystals, thermal media and other optical media
Nonlinear waves. Analysis of solitary waves and dispersive shock waves for integrable equations, such as Korteweg-de Vries equation, Nonlinear Schrodinger equation and their non integrable variants
Combustion theory and mathematical chemistry. Semi-analytical solutions for reaction-diffusion equations. Many chemical systems can be modelled by sets of reaction-diffusion equations, which are hard or impossible to analyse using the standard tools of combustion theory. This project will look at methods of approximating the governing equations by sets of ordinary differential equations and analysing the static and dynamic stability of the system