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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Nonlinear dispersive wave equations for microstructured solids; pp. 203–211

(Full article in PDF format) doi: 10.3176/proc.2015.3.01


Authors

Arkadi Berezovski

Abstract

Dispersion is a characteristic feature for wave propagation in microstructured solids. In the case of linear elasticity, dispersion effects are modelled by higher-order derivatives included into the wave equation. Nonlinear effects are also well known in wave propagation in solids. In principle, such effects may appear at the macroscale as well as at the microscale. The microstructural influence is often taken into account by the introduction of internal variables. This suggests that internal variables may behave nonlinearly. It is shown that the nonlinear behaviour of internal variables may lead at the macroscale to the Benjamin–Bona–Mahoney equation or the Camassa–Holm equation.

Keywords

dispersive wave equations, microstructured solids, nonlinearity.

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Current Issue: Vol. 68, Issue 3, 2019




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