nPatrick Sprenger, Department of Applied Mathematics, University of Colorado Boulder Generalized Riemann problems in dispersive hydrodynamics Nonlinear, dispersive wave phenomena are observed in a variety of physical contexts in nature and the laboratory. Mathematically, the dynamics are described by a dispersive hydrodynamic system---conservation laws modified by dispersion. Oftentimes, a multi-scale asymptotic expansion is employed to derive a single, scalar equation for a hydrodynamic quantity, from which we can infer approximate dynamics of the overarching system. We first study scalar models of dispersive hydrodynamics when dispersion is of higher order. Higher order dispersion in nonlinear scalar equations is present whenever spatial derivatives are higher than third order. The primary mathematical framework we utilize is Whitham modulation theory, an asymptotic method to describe the slow modulations of a periodic wave's parameters. We identify three new classes of DSWs solutions to the Kawahara equation---a weakly nonlinear model that contains both third and fifth order dispersive terms. Numerical and asymptotic studies of the DSW solutions to the Kawahara equation motivate a further comprehensive study of the Whitham modulation equations for the fifth order... https://calendar.colorado.edu/event/nonlinear_waves_seminar_-_patrick_sp...