Nonlinear waves: from beaches to lasers

The study of localized waves has a long history dating back to the discoveries in the 1800s by Russell, Boussinesq and Korteweg-deVries(KdV) describing water waves in shallow water. In the 1960s researchon the KdV equation led to the concept of solitons which are solitary waves which interact ``elastically’’. More recently both in fluid dynamics and nonlinear optics there has been considerable interest invarious aspects of localized waves. Some of the topics that will be briefly discussed include: cross-wave interactions in water waves,ultra-short pulse dynamics in lasers and nonlinear waves in optical lattices.