Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics
Abstract
We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: ∂x G(Hx). 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 G is an odd function of Hx. 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 G is an even function of Hx, we show that steady-state solutions are not permissible.
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