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SUMMARY:Exponential asymptotics for nonlinear waves in particle chains usi
 ng numerical analytic continuation - Christopher Lustri (Macquarie Univers
 ity)
DTSTART:20221111T150000Z
DTEND:20221111T170000Z
UID:TALK192485@talks.cam.ac.uk
DESCRIPTION:In the first half of the talk\, I will demonstrate the propaga
 tion of nonlinear waves in singularly-perturbed chains of particles with n
 earest-neighbour interactions (including systems such as diatomic Toda cha
 ins and woodpile Hertzian chains). The purpose of this analysis is to calc
 ulate exponentially small oscillations that appear due to Stokes' Phenomen
 on\, arising due to singularities in the analytic continuation of the lead
 ing-order solitary wave.\nAs the problems increase in complexity\, calcula
 ting the leading-order wave becomes impossible. I will demonstrate several
  methods for approximating the leading-order behaviour\, including a metho
 d known as the AAA algorithm\, and consider the effects of these approxima
 tions on the analytic continuation. Can the Stokes structure be recovered?
 &nbsp\;\nWe will see that the AAA method appears to be capable of reproduc
 ing the Stokes switching behaviour correctly\, despite having singularity 
 strength that is different to the "true" analytic continuation. I will att
 empt to explain how this can occur by considering a simple linear differen
 tial equation\, and show that -- for linear problems at least -- the metho
 d is trustworthy.
LOCATION:Seminar Room 2\, Newton Institute
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