University of Cambridge > > Applied and Computational Analysis > Small Dispersion Limit of the Camassa-Holm Equation

Small Dispersion Limit of the Camassa-Holm Equation

Add to your list(s) Download to your calendar using vCal

  • UserChristian Klein, UniversitĂ© de Bourgogne, Dijon
  • ClockFriday 27 November 2009, 14:00-15:00
  • HouseMR11, CMS.

If you have a question about this talk, please contact ai10.

The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture. We present a quantitative numerical comparison between the CH and the asymptotic solution. We illustrate differences to the well known small dispersion limit of the Korteweg-de Vries equation.

This talk is part of the Applied and Computational Analysis series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity