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Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities

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journal contribution
posted on 25.10.2019, 08:30 by FE Garbuzov, YM Beltukov, Karima KhusnutdinovaKarima Khusnutdinova
In this paper we study nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section within the scope of the general weakly-nonlinear model with quadratic and cubic nonlinearities. We derive the extended Boussinesq and Korteweg - de Vries - type equations and construct a family of approximate weakly-nonlinear soliton solutions with the help of the near-identity transformations. These solutions are compared with the results of direct numerical simulations of the original fully nonlinear problem formulation.

Funding

Russian Science Foundation under the grant no. 17-72-20201

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Theoretical and Mathematical Physics

Volume

202

Pages

319–333

Publisher

Springer Verlag

Version

AM (Accepted Manuscript)

Rights holder

© Pleiades Publishing, Ltd.

Publisher statement

This is a post-peer-review, pre-copyedit version of an article published in Theoretical and Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1134/S0040577920030046

Acceptance date

02/10/2019

Publication date

2020-04-06

Copyright date

2020

Notes

14 pages, 6 figures

ISSN

0040-5779

eISSN

1573-9333

Language

en

Depositor

Dr Karima Khusnutdinova Deposit date: 24 October 2019