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,
DCDS-A 36(6), 2991-3009 (2016)
Matt Coles and Dmitry Pelinovsky,
Loops of energy bands for Bloch waves in optical lattices,
Studies in Applied Mathematics 128(3), 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(8), 1753-1770 (2010)