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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Solitons in external fields - Maciej Zworski (UC B
erkeley)
DTSTART;TZID=Europe/London:20091207T160000
DTEND;TZID=Europe/London:20091207T170000
UID:TALK20926AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20926
DESCRIPTION:Solitons are the remarkably stable solitary wave s
olutions to certain nonlinear evolution equations\
, such as the nonlinear Schroedinger equation (NLS
) or the Korteveg-de Vries equation (KdV). They al
so enjoy a remarkable sociological stability by be
ing of interest to applied mathematicians\, PDE ex
perts\, algebraic geometers\, and representation t
heorists. The particle-like behaviour of solitons
is visible when external potentials are added to t
he original equations. That means that in addition
to self-interaction modeled by the nonlinearity\,
an external field is applied to the solitary wave
s. That can result in different kinds of phenomena
involving one or more solitons. I will describe r
esults obtained in collaboration with Justin Holme
r\, and with Justin Holmer and Galina Perelman\, o
n solitons for NLS and mKdV interacting with slowl
y varying external fields (semiclassical regime)\,
and with highly localized impurities (delta funct
ion potentials). The mathematical results are stri
kingly confirmed in numerical experiments which al
so suggest many open questions.
LOCATION:CMS\, MR15
CONTACT:Prof. Mihalis Dafermos
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