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We study the effect of a higher-order nonlinearity in the standardKuramoto-Sivashinsky equation: \partial_x \tilde G(H_x). We find that thestability of steady states depends on dv/dq, the derivative of the interfacevelocity on the wavevector q of the steady state. If the standard nonlinearityvanishes, coarsening is possible, in principle, only if \tilde G is an oddfunction of H_x. In this case, the equation falls in the category of thegeneralized Cahn-Hilliard equation, whose dynamical behavior was recentlystudied by the same authors. Instead, if \tilde G is an even function of H_x,we show that steady-state solutions are not permissible.Comment: 4 page

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