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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Modulational Stability for Equations of Whitham Ty
pe - Wesley Perkins (Lehigh University)
DTSTART;TZID=Europe/London:20220711T140000
DTEND;TZID=Europe/London:20220711T143000
UID:TALK175829AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175829
DESCRIPTION:In many applications it is natural to observe &ldq
uo\;locally periodic&rdquo\; patterns. Such patter
ns appear spatially periodic on local space/time s
cales while their fundamental wave characteristics
(such as amplitude or frequency) may slowly chang
e\, i.e.\, modulate\, over large space/time scales
. One powerful tool used to study such structures
is Whitham&rsquo\;s theory of wave modulations\, c
ommonly referred to as Whitham theory. While Whith
am theory lacks rigorous justification in general\
, its predictions match remarkably well with physi
cal and numerical observations\, and it has been r
igorously justified for a growing number of models
and equations. In the recent work by Binswanger e
t al.\, the authors use Whitham modulation theory
to analyze a generalized Whitham equation (i.e.\,
a Whitham-type equation with generalized nonlinear
flux and linear dispersion relation) and establis
h a modulational instability criterion. Building o
n their work\, this talk will rigorously connect t
he modulational instability criterion from the wor
k by Binswanger et al. to the spectral stability o
f long-wavelength perturbations of periodic travel
ing wave solutions to the generalized Whitham equa
tion\, thereby justifying Whitham modulation theor
y for the generalized Whitham equation. This provi
des a succinct justification of Whitham modulation
theory for the various equations that can be writ
ten in the form of the generalized Whitham equatio
n.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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