How do periodic structures affect nonlinear waves?
We are all familiar with the tendency of water waves to break in shallow water, for instance at the beach. Indeed, breaking is a universal behavior of solutions to first-order nonlinear hyperbolic PDEs, and manifests itself in phenomena ranging from traffic jams to shock waves.
Overview
Abstract
We are all familiar with the tendency of water waves to break in shallow water, for instance at the beach. Indeed, breaking is a universal behavior of solutions to first-order nonlinear hyperbolic PDEs, and manifests itself in phenomena ranging from traffic jams to shock waves. In the presence of periodic structures, such as an undulating seabed or a laminated composite, nonlinear waves can behave in a completely different manner, due to interactions between the wave and the underlying periodic structure. This interaction leads to an effective dispersion, resulting in the suppression of wave breaking and the formation of solitary waves. I will discuss a variety of physical settings in which this can occur, and show how it can be understood using multiple-scale analysis and numerical simulations.
Brief Biography
Prof. David Ketcheson is a Professor of Applied Mathematics and Computational Science at KAUST. He received his Ph.D. in 2009 from the University of Washington.