29 November 2004
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.
- Applied Analysis and Mechanics Seminar