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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dispersive shock waves\, traveling waves\, and def
ect solutions of the Kawahara equation - Patrick S
prenger (University of Cambridge)
DTSTART;TZID=Europe/London:20221115T110000
DTEND;TZID=Europe/London:20221115T120000
UID:TALK192800AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/192800
DESCRIPTION:Dispersive shock waves (DSWs) are multiscale\, non
linear waves that regularize singularities in disp
ersive hydrodynamic systems. A common mathematical
description DSWs is via a self-similar rarefactio
n wave solution of the Whitham modulation equation
s. In shallow water waves with sufficiently strong
surface tension\, numerical simulation of the Kaw
ahara equation reveals a coherent\, nonlinear wave
structure quite different from the typical DSW. I
n certain regimes\, this DSW is partially describe
d in terms of a discontinuous shock solution of th
e Whitham modulation equations that satisfies Rank
ine-Hugoniot jump conditions. Further analysis of
the jump conditions reveals families of traveling
wave solutions of the Kawahara equation that asymp
tote to distinct periodic orbits at infinity. Each
branch terminates at an equilibrium-to-periodic s
olution in which the equilibrium is the background
for a solitary wave that connects to the associat
ed periodic solution. This family of traveling wav
e solutions are used to compute traveling defect s
olutions\, which are localized on a periodic backg
round. Extensions of this work to Boussinesq syste
ms modeling gravity-capillary water waves will als
o be discussed.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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