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SUMMARY:Dispersive Shock Waves in the Benjamin-Ono Equation - Peter Miller
  (University of Michigan)
DTSTART:20221019T093000Z
DTEND:20221019T100000Z
UID:TALK182552@talks.cam.ac.uk
DESCRIPTION:The Benjamin-Ono equation is a model for internal water waves 
 in stratified fluids over an infinitely-deep lower layer. It is similar to
  the Korteweg-de Vries (KdV) equation\, but with a different dispersive te
 rm that is nonlocal\, involving the Hilbert transform. Like KdV\, it has a
  Lax pair\, although its inverse-scattering transform is not fully justifi
 ed in all details to date. This talk will describe the formation of disper
 sive shock waves in solutions of the Benjamin-Ono equation. Weak small-dis
 persion limits have been established for ``quasi'' initial-value problems 
 in the whole line setting by Miller and Xu and in the periodic setting by 
 Gassot. After describing those results\, we will discuss Whitham modulatio
 n theory due to Dobrokhotov and Krichever and explain some preliminary wor
 k on strong asymptotics to resolve the oscillations in the shock zone.
LOCATION:Seminar Room 1\, Newton Institute
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