Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities
journal contributionposted 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.
Russian Science Foundation under the grant no. 17-72-20201
- Mathematical Sciences