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SUMMARY:Modulation of Water Waves - Bridges\, T (University of Surrey)
DTSTART:20140808T130000Z
DTEND:20140808T140000Z
UID:TALK53673@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The lectures will provide an introduction to the theory of "mo
 dulation" and its role in the derivation of model equations\, such as the 
 KdV equation\, Boussinesq equation\, KP equation\, and Whitham modulation 
 equations\, and their role in the theory of water waves. The classical the
 ory of modulation\, such as Whitham modulation theory\, will be reviewed\,
  and a new approach will be introduced. The new approach is based on modul
 ation of background flow. Methodology that is key to the theory is symmetr
 y and conservation laws\, relative equilibria\, Hamiltonian and Lagrangian
  structures\, multiple scale perturbation theory\, and elementary differen
 tial geometry. By basing the theory on modulation of relative equilibria\,
  new settings are discovered for the emergence of KdV and other modulation
  equations. For example\, it is shown that the KdV equation can be a valid
  model for deep water as well as shallow water. The lectures are introduct
 ory\, and no prior knowledge is assumed.\n\n
LOCATION:CMS\, RM9
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