The BBM equation is a nonlinear dispersive scalar PDE related to the KdV equation. However, it has a non-convex dispersion relation that introduces a variety of novel wave structures. These waves are highlighted by considering numerical solutions of Riemann problems, in which a smoothed step function initial condition u(x,0) exhibits long-time behavior that is a challenge for asymptotic analysis and the theory of dispersive hydrodynamics. In this talk, I describe the new waves and the analysis explaining their structure. This is joint work with Thibault Congy, Gennady El and Mark Hoefer.

Zoom meeting ID: 802 764 2791