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SUMMARY:Small Dispersion Limit of the Camassa-Holm Equation - Christian Kl
 ein\, Université de Bourgogne\, Dijon
DTSTART:20091127T140000Z
DTEND:20091127T150000Z
UID:TALK21685@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:The small dispersion limit of solutions to the Camassa-Holm (C
 H)\n equation is characterized by the appearance of a zone of rapid\n modu
 lated oscillations. An asymptotic description of these\n oscillations is g
 iven\, for short times\, by the one-phase\n solution to the CH equation\, 
  where the branch points of the corresponding elliptic curve depend on the
  physical\n coordinates via the  Whitham equations. We present a conjectur
 e for  the phase of the asymptotic solution. A numerical\n study of this l
 imit for smooth hump-like initial data provides strong  evidence for the v
 alidity of this conjecture. We present a\n quantitative numerical comparis
 on between the CH\n and the asymptotic solution. We illustrate differences
  to the well known small dispersion limit of the Korteweg-de Vries equatio
 n.
LOCATION:MR11\, CMS
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