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SUMMARY:Dispersive Shock Waves - Mark Ablowitz\, University of Colorado
DTSTART:20070720T150000Z
DTEND:20070720T160000Z
UID:TALK7712@talks.cam.ac.uk
CONTACT:Nigel Peake
DESCRIPTION:\nDispersive shock waves (DSW's) are described by a slowly var
 ying one-phase periodic wave train that connects solitons at one edge to l
 inear dispersive waves at the other. DSW's are associated with equations w
 hich are 'regularized' by a small dispersive term. This is different from 
 viscous shock waves (VSW's) which are characterized by rapid localized cha
 nges in the underlying physical quantities. Equations with VSW's are regul
 arized by a small viscous term. Recent laboratory experiments in Bose-Eins
 tein condensates and nonlinear optics have demonstrated both single phase 
 DSW and complex-interacting multiphase behavior. Numerical and analytical 
 results explain many of the observed phenomena. If time permits\, a reform
 ulation of the water wave equations in terms of a novel nonlocal system wi
 ll be discussed. Special cases include shallow and deep water asymptotic r
 eductions. Localized waves including two dimensional water wave lumps to t
 he nonlinear water wave equations with sufficient surface tension are nume
 rically obtained.\n
LOCATION:MR5\, Centre for Mathematical Sciences
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