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SUMMARY:Dispersive Riemann problem for the Benjamin-Bona-Mahony equation -
  Thibault Congy (Northumbria University)
DTSTART:20220715T140000Z
DTEND:20220715T143000Z
UID:TALK175913@talks.cam.ac.uk
DESCRIPTION:The Benjamin-Bona-Mahony (BBM) equation $u_t + uu_x = u_{xxt}$
  as a model for unidirectional\, weakly nonlinear dispersive shallow water
  wave propagation is asymptotically equivalent to the celebrated Korteweg-
 de Vries (KdV) equation while providing more satisfactory short-wave behav
 ior in the sense that the linear dispersion relation is bounded for the BB
 M equation\, but unbounded for the KdV equation. However\, the BBM dispers
 ion relation is nonconvex\, a property that gives rise to a number of intr
 iguing features markedly different from those found in the KdV equation\, 
 providing the motivation for the study of the BBM equation as a distinct d
 ispersive regularization of the Hopf equation.\nThe dynamics of the smooth
 ed step initial value problem or dispersive Riemann problem for BBM equati
 on are studied using asymptotic methods and numerical simulations. I will 
 present the emergent wave phenomena for this problem which can be split in
 to two categories: classical and nonclassical. Classical phenomena include
  dispersive shock waves and rarefaction waves\, also observed in convex Kd
 V-type dispersive hydrodynamics. Nonclassical features are due to nonconve
 x dispersion and include the generation of two-phase linear wavetrains\, e
 xpansion shocks\, solitary wave shedding\, dispersive Lax shocks\, DSW imp
 losion and the generation of incoherent solitary wavetrains.\nThis present
 ation is based on a joint work with G. El\, M. Shearer and M. Hoefer.
LOCATION:Seminar Room 1\, Newton Institute
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