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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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