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CATEGORIES:Academics,Lectures & conferences
DESCRIPTION:Speaker: Nikola Stoilov\, University of Bourgogne\, Dijon (Fran
ce)\n\nTitle: Numerical studies of the Davey-Stewartson and Zakharov-Kuznet
sov equations\n\nAbstract: In this work we look at the behaviour of the Dav
ey-Stewartson (DS) and Zakharov Kuznetsov (ZK) equations\, using advanced n
umerical tools. As a nonlinear dispersive PDE and a generalization of the n
on-linear SchrÃ¶dinger equation\, DS has explicit solutions that develop a s
ingularity in finite time. We will discuss the long time behaviour and pote
ntial blow-up of solutions to the focusing Davey-Stewartson II equation for
various initial data and propose a conjecture describing the rate and solu
tion profiles near the singularity. We will also look at integrable propert
ies of DS and the associated scattering problem. ZK is also a nonlinear dis
persive PDE and can be seen as a generalisation of the KdV\, however it is
not integrable. We demonstrate its behaviour as a dispersive PDE and will l
ook at blow-up\, soliton resolution and soliton interaction and discuss how
the non-integrability transpires in these cases. We propose several conjec
tures for the long term behaviour.\n\nBased on joint works with Christian K
lein and Ken McLaughlin and Svetlana Roudenko.\n\nZoom Link: https://fiu.zo
om.us/j/94146267582?pwd=SWpaZHFmM2pZS1VXb3pNa1Uyb3hVdz09
DTEND:20210521T150000Z
DTSTAMP:20221206T162055Z
DTSTART:20210521T140000Z
LOCATION:
SEQUENCE:0
SUMMARY:Applied Math Seminar: Numerical studies of the Davey-Stewartson and
Zakharov-Kuznetsov equations by Nikola Stoilov
UID:tag:localist.com\,2008:EventInstance_36767229447734
URL:https://calendar.fiu.edu/event/applied_math_seminar_numerical_studies_o
f_the_davey-stewartson_and_zakharov-kuznetsov_equations_by_nikola_stoilov
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