Broadly, I study Partial Differential Equations.
A little more specifically I use techniques from analysis to study qualitative behaviour of solutions to the Nonlinear Schrödinger Equation.
Matt Coles and Stephen Gustafson, A Degenerate Edge Bifurcation in the 1D Linearized Nonlinear Schrödinger Equation,
Matt Coles and Dmitry Pelinovsky,
Loops of energy bands for Bloch waves in optical lattices,
Studies in Applied Mathematics 128, 300-336 (2012)
M.P. Coles, D.E. Pelinovsky and P.G. Kevrekidis,
Excited states in the large density limit: a variational approach,
Nonlinearity 23, 1753-1770 (2010)