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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Dispersive Shock Waves - Mark Ablowitz\, Universit
y of Colorado
DTSTART;TZID=Europe/London:20070720T160000
DTEND;TZID=Europe/London:20070720T170000
UID:TALK7712AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/7712
DESCRIPTION:\nDispersive shock waves (DSW's) are described by
a slowly varying one-phase periodic wave train tha
t connects solitons at one edge to linear dispersi
ve waves at the other. DSW's are associated with e
quations which are 'regularized' by a small disper
sive term. This is different from viscous shock wa
ves (VSW's) which are characterized by rapid local
ized changes in the underlying physical quantities
. Equations with VSW's are regularized by a small
viscous term. Recent laboratory experiments in Bos
e-Einstein condensates and nonlinear optics have d
emonstrated both single phase DSW and complex-inte
racting multiphase behavior. Numerical and analyti
cal results explain many of the observed phenomena
. If time permits\, a reformulation of the water w
ave equations in terms of a novel nonlocal system
will be discussed. Special cases include shallow a
nd deep water asymptotic reductions. Localized wav
es including two dimensional water wave lumps to t
he nonlinear water wave equations with sufficient
surface tension are numerically obtained.\n
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Nigel Peake
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