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SUMMARY:Modulation Instability of undular bores in Whitham-Boussinesq syst
 ems and revealing characteristics of Stokes wave trains and solitary waves
  associated with these systems. - Rosa  Vargas-Magana (Universidad Naciona
 l Autonoma de Mexico (UNAM))
DTSTART:20220713T100000Z
DTEND:20220713T103000Z
UID:TALK175865@talks.cam.ac.uk
DESCRIPTION:Modulation instability of the Stokes wave solution of Whitham-
 Boussinesq systems derived from the water wave equations is analyzed in an
  attempt to examine Benjamin-Feir Instability for these systems and its co
 nnection with modulational instability of undular bores previously identif
 ied for these systems.&nbsp\; These Whitham-Boussinesq systems are in the 
 weakly nonlinear limit\, but with the full linear dispersion of the water 
 wave equations.&nbsp\; This instability is related to previous work on the
  modulational instability of dispersive shock wave solutions of the Whitha
 m-Boussinesq equations and of the full water wave equations.&nbsp\; The mo
 dulation instability on Stokes waves is analyzed for the previously identi
 fied wavenumbers associated with the water wave dispersive shock wave. We 
 also examine the existence of solitary wave solutions of the Whitham-Bouss
 inesq systems with details given of their shape and amplitude-velocity rel
 ation. Finally\, the implications of these results for the Whitham-Boussin
 esq systems with the addition of surface tension for gravity-capillary RDS
 W and CDSW solutions are discussed\, which is work in progress.\nThis is j
 oint work with Prof. Noel Smyth from the University of Edinburgh\, Prof. T
 im Marchant from the University of Melbourne\, and Dr. Marcelo Flamarion f
 rom the Universidade Federal Rural de Pernambu.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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