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SUMMARY:Universal description of dispersive shock waves - Thibault Congy (
 Northumbria University)
DTSTART:20221206T143000Z
DTEND:20221206T150000Z
UID:TALK183779@talks.cam.ac.uk
DESCRIPTION:The nonlinear nonlinear Schr&ouml\;dinger (NLS) equation and t
 he Whitham modulation equations both describe slowly varying\, locally per
 iodic nonlinear wavetrains\, albeit in differing amplitude-frequency domai
 ns. Taking advantage of the overlap regime for the applicability of the NL
 S equation and the Whitham modulation theory\, we develop a universal anal
 ytical description of dispersive shock waves (DSWs) generated in Riemann p
 roblems for a broad class of integrable and non-integrable nonlinear dispe
 rsive equations. The proposed method extends and complements the DSW fitti
 ng theory prescribing the motion of DSW edges. We consider several represe
 ntative physically relevant examples illustrating efficacy of the develope
 d general theory. Comparisons with direct numerical simulations show that 
 inclusion of higher order terms in the NLS equation enables a remarkably a
 ccurate description of the DSW modulation in a broad vicinity of the harmo
 nic\, small amplitude\, edge.This is joint work with Gennady El\, Mark Hoe
 fer and Michael Shearer.
LOCATION:Seminar Room 1\, Newton Institute
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