Nonlinear, nondispersive surface waves

PDE Seminar
Tuesday, April 22, 2014 - 15:05
1 hour (actually 50 minutes)
Skile 006
University California, Davis
Surface waves are waves that propagate along a boundary or interface, with energy that is localized near the surface. Physical examples are water waves on the free surface of a fluid, Rayleigh waves on an elastic half-space, and surface plasmon polaritons (SPPs) on a metal-dielectric interface. We will describe some of the history of surface waves and explain a general Hamiltonian framework for their analysis. The weakly nonlinear evolution of dispersive surface waves is described by well-known PDEs like the KdV or nonlinear Schrodinger equations. The nonlinear evolution of nondispersive surface waves, such as Rayleigh waves or quasi-static SPPs, is described by nonlocal, quasi-linear, singular integro-differential equations, and we will discuss some of the properties of these waves, including the formation of singularities on the boundary.