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SUMMARY:Hamiltonian shocks - Russell Arnold (UNC Chapel Hill and RIMS)
DTSTART:20221117T110000Z
DTEND:20221117T120000Z
UID:TALK192806@talks.cam.ac.uk
DESCRIPTION:The nature of wave interaction in a continuum dynamical model 
 may undergo a qualitative change in certain asymptotic regimes\, most nota
 bly when linearity or complete integrability is introduced. This occurs in
  particular when the mKdV equation is used to model the unidirectional dis
 persive dynamics of two layer shallow water fluid flow near a critical int
 erfacial height. Motivated by the symmetric properties of conjugate states
  which have been observed for the MCC equations in the Boussinesq limit\, 
 the work to be presented elucidates a more subtle qualitative shift\, resi
 ding purely in the dispersionless reduction of a system\, which determines
  whether a Hamiltonian undercompressive shock\, representing a kink\, will
  interact with a gradual background wave without producing a loss of regul
 arity\, which would take the form of a classical dispersive shock. This pr
 operty is also related to an infinitude of conservation laws\, drawing a f
 urther parallel to the integrable case. &nbsp\;This is a joint work with R
 oberto Camassa and Lingyun Ding.
LOCATION:Seminar Room 2\, Newton Institute
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