On nonlinear dynamics of neutral modes in elastic waves in granular media

Article

Strunin, D. V. and Ali, A. A.. 2016. "On nonlinear dynamics of neutral modes in elastic waves in granular media." Journal of Coupled Systems and Multiscale Dynamics. 4 (3). https://doi.org/10.1166/jcsmd.2016.1105
Article Title

On nonlinear dynamics of neutral modes in elastic waves in granular media

ERA Journal ID210840
Article CategoryArticle
AuthorsStrunin, D. V. (Author) and Ali, A. A. (Author)
Journal TitleJournal of Coupled Systems and Multiscale Dynamics
Journal Citation4 (3)
Number of Pages7
Year2016
Place of PublicationUnited States
ISSN2330-152X
2330-1538
Digital Object Identifier (DOI)https://doi.org/10.1166/jcsmd.2016.1105
Web Address (URL)http://www.aspbs.com/jcsmd
Abstract

We analyse a passive system featuring a neutrally stable short-wavelength mode. The system is modelled by the Nikolaevskiy equation relevant to certain type of elastic waves, reaction-diffusion systems and convection. Due to the nonlinear coupling between the time-dependent Fourier modes, the system exhibits asymptotically slow evolution towards either zero or non-zero steady state depending on the initial condition and the neutral wave number. Using the centre manifold technique, we deduced that the decay law is that of inverse square root of time. The result is confirmed by the computations of the dynamical system for the Fourier modes.

Keywordsmathematical, physical & engineering sciences, life, climate, environmental sciences
ANZSRC Field of Research 2020490109. Theoretical and applied mechanics
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Byline AffiliationsComputational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
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