17:00
Coherent structures, or defects, are interfaces between wave trains with
possibly different wavenumbers: they are time-periodic in an appropriate
coordinate frame and connect two, possibly different, spatially-periodic
travelling waves. We propose a classification of defects into four
different classes which have all been observed experimentally. The
characteristic distinguishing these classes is the sign of the group
velocities of the wave trains to either side of the defect, measured
relative to the speed of the defect. Using a spatial-dynamics description
in which defects correspond to homoclinic and heteroclinic orbits, we then
relate robustness properties of defects to their spectral stability
properties. If time permits, we will also discuss how defects interact with
each other.