Discontinuity, Nonlinearity, and Complexity
Decay in Systems with Neutral ShortWavelength Stability: The Presence of a Zero Mode
Discontinuity, Nonlinearity, and Complexity 10(2) (2021) 195205  DOI:10.5890/DNC.2021.06.003
Adham A. Ali , Fatima Z. Ahmed
Department of Mathematics, Kirkuk University,
Kirkuk, Iraq
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Abstract
A characteristic feature of seismic waves is the presence of dominant frequency/wave number in the spectrum. A wellknown model for such waves is the Nikolaevskiy equation, which is also applicable to some reactiondiffusion systems and RayleighBenard convection. For the critical case when there is one neutral mode, we describe the dynamics of the Fourier modes (elastic waves) under the Nikolaevskiy equation using the centre manifold technique. After quickly attracted to the surface (manifold), the modes then evolve slow algebraic decay. An inverse squareroot law for the decaying regime is obtained. The result is confirmed by direct computations of the dynamical system for the modes.
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