BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Dispersive shock waves\, traveling waves\, and defect solutions of
  the Kawahara equation - Patrick Sprenger (University of Cambridge)
DTSTART:20221115T110000Z
DTEND:20221115T120000Z
UID:TALK192800@talks.cam.ac.uk
DESCRIPTION:Dispersive shock waves (DSWs) are multiscale\, nonlinear waves
  that regularize singularities in dispersive hydrodynamic systems. A commo
 n mathematical description DSWs is via a self-similar rarefaction wave sol
 ution of the Whitham modulation equations. In shallow water waves with suf
 ficiently strong surface tension\, numerical simulation of the Kawahara eq
 uation reveals a coherent\, nonlinear wave structure quite different from 
 the typical DSW. In certain regimes\, this DSW is partially described in t
 erms of a discontinuous shock solution of the Whitham modulation equations
  that satisfies Rankine-Hugoniot jump conditions. Further analysis of the 
 jump conditions reveals families of traveling wave solutions of the Kawaha
 ra equation that asymptote to distinct periodic orbits at infinity. Each b
 ranch terminates at an equilibrium-to-periodic solution in which the equil
 ibrium is the background for a solitary wave that connects to the associat
 ed periodic solution. This family of traveling wave solutions are used to 
 compute traveling defect solutions\, which are localized on a periodic bac
 kground. Extensions of this work to Boussinesq systems modeling gravity-ca
 pillary water waves will also be discussed.
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR