Zoom Meeting: https://unm.zoom.us/j/93108685209 

Password: contact the organizer

Title: Whitham modulation theory for dispersive hydrodynamic models with full linear dispersion

Abstract: In his work in the 1960’s, Whitham introduced a scalar, full-dispersion model of surface water waves that exactly match the linear dispersion relation for the water wave problem. To do this, he replaced the linear dispersive term in the Korteweg-de Vries equation with a nonlocal pseudodifferential operator that defines the linear dispersion for gravity water waves. Following this approach, we consider a class of dispersive hydrodynamic models whose linear dispersion is “engineered” to faithfully represent linear dispersive wave phenomena. With these models in hand, we utilize Whitham modulation theory to derive conservation laws that describe slow modulations of periodic wave trains. I will discuss how this framework can be utilized to study the modulational (in)stability of periodic wave trains and how it can be used to obtain novel traveling wave solutions that are represented by localized defects on a background periodic wave.  

Bio: Patrick Sprenger received his PhD in applied mathematics from the University of Colorado Boulder in 2019. Following his PhD, he held a postdoctoral fellowship in the Mathematics Department at North Carolina State University. In 2022, he began a position as an INI-Simon’s Postdoctoral Fellow at the Isaac Newton Institute for Mathematical Sciences,  University of Cambridge.