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SUMMARY:On the extended KdV equation and near-identity transformations for
  strain waves - Karima Khusnutdinova (Loughborough University)
DTSTART:20220718T103000Z
DTEND:20220718T110000Z
UID:TALK176078@talks.cam.ac.uk
DESCRIPTION:We study long nonlinear longitudinal bulk strain waves in a hy
 perelastic rod of circular cross-section within the scope of the general w
 eakly-nonlinear elasticity. We systematically derive the extended Boussine
 sq and Korteweg-de Vries (eKdV) equations and construct a family of approx
 imate weakly-nonlinear soliton solutions with the help of near-identity tr
 ansformations reducing the eKdV equation to the Gardner equation. These so
 lutions are compared with the results of direct numerical simulations of t
 he original nonlinear problem formulation\, showing excellent agreement wi
 thin the range of their asymptotic validity (waves of small amplitude) and
  extending their relevance beyond it (to the waves of moderate amplitude\,
  e.g. table-top solitons) as a very good initial guess. Recently\, the gen
 eration of undular bores in polymer bars following tensile fracture was re
 gistered using high-speed pointwise photoelasticity. We show that a viscoe
 lastic extended Korteweg - de Vries (veKdV) equation provides a very good 
 agreement with the key observed experimental features for a suitable choic
 e of material parameters.&nbsp\; Based on joint papers with F.E. Garbuzov\
 , Y.M. Beltukov\, C.G. Hooper\, P.D. Ruiz and J.M. Huntley.
LOCATION:Seminar Room 1\, Newton Institute
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