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DTSTAMP:20260516T140650Z
SUMMARY:Nelder Fellow Series: Professor Triantafyllos Akylas (MIT)
DESCRIPTION:Professor Triantafyllos Akylas on: Exponential asymptotics: app
 lications to water waves\nAbstract: This Lecture will focus on application
 s of the wavenumber exponential asymptotics technique introduced in Lectur
 e I\, to two problems of water waves: (i) gravity-capillary solitary waves
  in shallow water for Bond number < 1/3\; (ii) bifurcation of gravity-capi
 llary solitary waves at the minimum phase speed on water of finite or infi
 nite depth.\nIn (i)\, the classical weakly nonlinear long-wave expansion f
 ails to capture the short-scale oscillations which arise at the tails due 
 to capillary waves that propagate at the same speed as the main hump.  Us
 ing the wavenumber technique\, these tails are computed asymptotically\, i
 n good agreement with direct numerical computations.  Thus\, in the prese
 nce of small surface tension (Bond < 1/3)\, solitary waves on shallow wate
 r are non-local.\nIn (ii)\, the bifurcating solitary waves are in the form
  of envelope solitons of the nonlinear Schrödinger (NLS) equation with  
 carrier (crests) propagating at the same speed as the envelope.  Here\, e
 xponential asymptotics is required in order to specify the phase of the cr
 ests relative to the envelope.  It is shown that only two branches of sym
 metric solitary waves bifurcate at zero amplitude.  By contrast\, there i
 s a rich variety of symmetric and asymmetric solitary wave solutions that 
 bifurcate at small but finite amplitude.  The asymptotic predictions are 
 confirmed by direct numerical computations. 
URL:https://www.imperial.ac.uk/events/189577/nelder-fellow-series-professor
 -triantafyllos-akylas-2/
DTSTART;TZID=Europe/London:20250305T120000
DTEND;TZID=Europe/London:20250305T140000
LOCATION:130\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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