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Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics

Paolo Politi·Chaouqi Misbah
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Abstract

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: \partial_x \tilde G(H_x). We find that the stability of steady states depends on dv/dq, the derivative of the interface velocity on the wavevector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if \tilde G is an odd function of H_x. In this case, the equation falls in the category of the generalized Cahn-Hilliard equation, whose dynamical behavior was recently studied by the same authors. Instead, if \tilde G is an even function of H_x, we show that steady-state solutions are not permissible.

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Paolo Politi, Chaouqi Misbah. 2006-10-25. Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics. https://doi.org/10.1103/physreve.75.027202

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