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CATEGORIES:Applied Mathematics Seminar Series
SUMMARY:Exponential asymptotics and homoclinic snaking in
continuous and discrete systems - Andrew Dean (Uni
versity of Leeds)
DTSTART:20131014T130000Z
DTEND:20131014T140000Z
UID:TALK1211AT
URL:/talk/index/1211
DESCRIPTION:Homoclinic snaking of localized patterns has been
observed in a variety of experimental and theoreti
cal contexts. The phenomenon\, in which a multipli
city of localized states exists within an exponent
ially small parameter range\, is due to a slowly v
arying amplitude ’locking’ to the underlying\, fas
t-scale pattern. Through a careful asymptotic anal
ysis of the one-dimensional Swift-Hohenberg equat
ion\, we show how the conventional method of multi
ple scales near bifurcation must be extended to in
corporate exponentially small eﬀects if a complete
asymptotic description of snaking behaviour is to
be achieved. We then apply similar techniques to
study one-dimensional snaking on a square lattice\
, in which the slow amplitude locks onto the spati
al grid\, and show that the snaking region is non-
zero only when the solution is oriented at an angl
e which has a rational or infinite tangent.
LOCATION:Arts Lecture Room 4
CONTACT:Alexandra Tzella
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