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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Exponential asymptotics for nonlinear waves in par
ticle chains using numerical analytic continuation
- Christopher Lustri (Macquarie University)
DTSTART;TZID=Europe/London:20221111T150000
DTEND;TZID=Europe/London:20221111T170000
UID:TALK192485AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/192485
DESCRIPTION:In the first half of the talk\, I will demonstrate
the propagation of nonlinear waves in singularly-
perturbed chains of particles with nearest-neighbo
ur interactions (including systems such as diatomi
c Toda chains and woodpile Hertzian chains). The p
urpose of this analysis is to calculate exponentia
lly small oscillations that appear due to Stokes'
Phenomenon\, arising due to singularities in the a
nalytic continuation of the leading-order solitary
wave.\nAs the problems increase in complexity\, c
alculating the leading-order wave becomes impossib
le. I will demonstrate several methods for approxi
mating the leading-order behaviour\, including a m
ethod known as the AAA algorithm\, and consider th
e effects of these approximations on the analytic
continuation. Can the Stokes structure be recovere
d? \;\nWe will see that the AAA method appears
to be capable of reproducing the Stokes switching
behaviour correctly\, despite having singularity
strength that is different to the "true" analytic
continuation. I will attempt to explain how this c
an occur by considering a simple linear differenti
al equation\, and show that -- for linear problems
at least -- the method is trustworthy.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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