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CATEGORIES:Theoretical Physics Seminars
SUMMARY:Solitonic dispersive hydrodynamics and modulation
theory - Gennady El (Northumbria)
DTSTART:20181206T134500Z
DTEND:20181206T150000Z
UID:TALK3315AT
URL:/talk/index/3315
DESCRIPTION:Ubiquitous nonlinear waves in dispersive media inc
lude localized solitons and extended hydrodynamic
states such as dispersive shock waves. Despite the
ir physical prominence and the development of thor
ough theoretical and experimental investigations o
f each separately\, experiments and a unified theo
ry of solitons and dispersive hydrodynamics are la
cking. In my talk\, I will present a general solit
on-mean field theory to describe the propagation
of solitons in macroscopic hydrodynamic flows. Und
er the scale separation assumption of nonlinear wa
ve (Whitham) modulation theory\, the highly nontri
vial nonlinear interaction\nbetween the soliton an
d the evolving hydrodynamic barrier is described i
n terms of self-similar\, simple wave solutions to
an asymptotic reduction of the Whitham partial di
fferential equations associated with the original
dispersive hydrodynamics. Two adiabatic invariant
s of motion are identified that predict trapping
or transmission of solitons by hydrodynamic states
. The result of solitons incident upon smooth expa
nsion waves or compressive\, rapidly oscillating d
ispersive shock waves is the same\, an effect term
ed hydrodynamic reciprocity. If the governing equa
tion is integrable the soliton trapping has non-tr
ivial implications from the viewpoint of inverse s
cattering theory.\n\nAlong with theoretical develo
pments I will also present results of experiments
on viscous fluid conduits that quantitatively conf
irm the soliton-mean field theory with broader imp
lications for nonlinear optics\, superfluids\, geo
physical fluids\, and other dispersive hydrodynami
c media. \n \n \n This is joint work with Mark
Hoefer (University of Colorado\, Boulder).
LOCATION:Theory Library
CONTACT:Mike Gunn
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