Towards a Classification of Defects in Oscillatory Media
by
Bjorn Sandstede
Ohio State University
Coauthors: Arnd Scheel

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 connections of an ill-posed pseudo-elliptic equation, we then relate robustness properties of defects to their spectral stability properties. If time permits, we shall also discuss how different defects interact with each other.

Date received: October 3, 2003