Nonlinear waves in two-dimensional lattices

Project description

The localisation of energy and its transport in chains and across lattices of great physical interest in many applications. The mechanisms by which this occurs have been widely studied in one-dimensional systems; however, in two- and three-dimensional systems a greater variety of waves and wave phenomena can be observed; for example, waves can be localised in one or both directions.

For example, motion can be localised to specific lines or planes in a crystal lattice. Square lattices are widely studied, but the analysis of hexagonal lattices - both triangular and honeycomb are more complicated. The project will involve numerical techniques to the study such systems, as well as asymptotic analysis of partial differential equations.