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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Contour integral solutions of the parabolic wave e
 quation and applications to canonical scattering p
 roblems - David Hewett (University College London)
DTSTART;TZID=Europe/London:20230207T153000
DTEND;TZID=Europe/London:20230207T161500
UID:TALK194767AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194767
DESCRIPTION:We present a simple\, systematic construction and 
 analysis of solutions of the two dimensional parab
 olic (or paraxial) wave equation that exhibit far-
 field localisation near certain algebraic plane cu
 rves. Our solutions are complex contour integral s
 uperpositions of elementary plane wave solutions w
 ith polynomial phase\, the desired localisation be
 ing associated with the coalescence of saddle poin
 ts. Our solutions provide a unified framework in w
 hich to describe some classical phenomena in two-d
 imensional high frequency wave propagation\, inclu
 ding smooth and cusped caustics\, whispering galle
 ry and creeping waves\, and tangent ray diffractio
 n by a smooth boundary. We also study a subclass o
 f solutions exhibiting localisation near a cubic p
 arabola\, and discuss their possible relevance to 
 the study of the canonical inflection point proble
 m governing the transition from whispering gallery
  waves to creeping waves.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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