BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dispersive Riemann problem for the Benjamin-Bona-M
ahony equation - Thibault Congy (Northumbria Unive
rsity)
DTSTART;TZID=Europe/London:20220715T150000
DTEND;TZID=Europe/London:20220715T153000
UID:TALK175913AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175913
DESCRIPTION:The Benjamin-Bona-Mahony (BBM) equation $u_t + uu_
x = u_{xxt}$ as a model for unidirectional\, weakl
y nonlinear dispersive shallow water wave propagat
ion is asymptotically equivalent to the celebrated
Korteweg-de Vries (KdV) equation while providing
more satisfactory short-wave behavior in the sense
that the linear dispersion relation is bounded fo
r the BBM equation\, but unbounded for the KdV equ
ation. However\, the BBM dispersion relation is no
nconvex\, a property that gives rise to a number o
f intriguing features markedly different from thos
e found in the KdV equation\, providing the motiva
tion for the study of the BBM equation as a distin
ct dispersive regularization of the Hopf equation.
\nThe dynamics of the smoothed step initial value
problem or dispersive Riemann problem for BBM equa
tion are studied using asymptotic methods and nume
rical simulations. I will present the emergent wav
e phenomena for this problem which can be split in
to two categories: classical and nonclassical. Cla
ssical phenomena include dispersive shock waves an
d rarefaction waves\, also observed in convex KdV-
type dispersive hydrodynamics. Nonclassical featur
es are due to nonconvex dispersion and include the
generation of two-phase linear wavetrains\, expan
sion shocks\, solitary wave shedding\, dispersive
Lax shocks\, DSW implosion and the generation of i
ncoherent solitary wavetrains.\nThis presentation
is based on a joint work with G. El\, M. Shearer a
nd M. Hoefer.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
END:VEVENT
END:VCALENDAR