Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics.
We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: partial differentialxG(Hx). We find that the stability of steady states depends on dv/dq , the derivative of the interface velocity on the wave vector 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. Alternatively, if G is an even function of Hx, we show that steady-state solutions are not permissible.
Politi
Paolo
P
Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy. paolo.politi@isc.cnr.it
Misbah
Chaouqi
C