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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Reductions of (2+1) and (3+1) Dimensional Kadomts
ev- Petviashvili Type Equations and Dispersive Sho
ck Waves - Ali Demirci (Instanbul Technical Univer
sity)
DTSTART;TZID=Europe/London:20220714T110000
DTEND;TZID=Europe/London:20220714T113000
UID:TALK175877AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175877
DESCRIPTION:In our recent works\, dispersive shock waves (DSWs
) in the (2+1) and (3+1) dimensional Kadomtsev- Pe
tviashvili type equations (KP\, modified KP and Ga
rdner-KP equations) were studied with a step-like
initial condition along some chosen special fronts
. By using a similarity reduction\, the problem of
studying DSWs in the multidimensional equations r
educed to finding DSW solution of a (1+1) dimensio
nal equations. Whitham modulation equations were d
erived which describes DSW evolution in the reduce
d equations by using the method of multiple scales
. These equations were written in terms of appropr
iate Riemann type variables to obtain the Whitham
systems of the reduceded (1+1) dimensional equatio
ns. DSW solutions which were obtained from the num
erical solutions of the Whitham systems and the di
rect numerical solution of the reduced (1+1) dimen
sional equations were compared. In this comparison
\, an agreement was found between these solutions.
Also\, some physical qualitative results about DS
Ws in the reduced equations were presented. DSW so
lutions in the reduced equations provide some info
rmation about DSW behavior along the intial fronts
in the reduced equations. In this talk\, I will c
ompare the similarities and distinctions of DSW so
lutions of these reduced (1+1) dimensional equatio
ns. I will also discuss how DSW solutions of these
reduced equations can be used to construct DSW so
lutions of the original mutidimensional equations.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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