Abstract
Boussinesq-type equations arise in many areas of fluid and solid mechanics where nonlinearities and dispersion are taken into account. In this paper the analysis of two Boussinesq-type models is presented. One model describes propagation of waves in microstructured solids and another one – waves in biomembranes. The main difference between these equations is the structure of the nonlinearities – in case of the microstructure model these are in terms of displacement gradients and in case of the biomembrane – in terms of displacements. Numerical analysis is carried out and differences in the solutions are discussed. Due to the nonlinear character of biomembranes made of lipids, the smaller solitons in biomembranes may travel faster than higher solitons.
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