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SUMMARY:Modulational Stability for Equations of Whitham Type - Wesley Perk
 ins (Lehigh University)
DTSTART:20220711T130000Z
DTEND:20220711T133000Z
UID:TALK175829@talks.cam.ac.uk
DESCRIPTION:In many applications it is natural to observe &ldquo\;locally 
 periodic&rdquo\; patterns. Such patterns appear spatially periodic on loca
 l space/time scales while their fundamental wave characteristics (such as 
 amplitude or frequency) may slowly change\, i.e.\, modulate\, over large s
 pace/time scales. One powerful tool used to study such structures is Whith
 am&rsquo\;s theory of wave modulations\, commonly referred to as Whitham t
 heory. While Whitham theory lacks rigorous justification in general\, its 
 predictions match remarkably well with physical and numerical observations
 \, and it has been rigorously justified for a growing number of models and
  equations. In the recent work by Binswanger et al.\, the authors use Whit
 ham modulation theory to analyze a generalized Whitham equation (i.e.\, a 
 Whitham-type equation with generalized nonlinear flux and linear dispersio
 n relation) and establish a modulational instability criterion. Building o
 n their work\, this talk will rigorously connect the modulational instabil
 ity criterion from the work by Binswanger et al. to the spectral stability
  of long-wavelength perturbations of periodic traveling wave solutions to 
 the generalized Whitham equation\, thereby justifying Whitham modulation t
 heory for the generalized Whitham equation. This provides a succinct justi
 fication of Whitham modulation theory for the various equations that can b
 e written in the form of the generalized Whitham equation.
LOCATION:Seminar Room 1\, Newton Institute
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