Stabilized Kuramoto-Sivashinsky system - art. no. 046304

A model consisting of a mixed Kuramoto-Sivashinsky-Korteweg-de Vries equati on, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to a description of surface waves on multilayered liquid films. The extra equation makes it possible to stabilize the zero solution in the model, thus opening the way to the existence of stable solitary puls es. By means of perturbation theory, treating the dissipation and the insta bility-generating gain in the model (but not the linear coupling between di e two waves) as small perturbations, and making use of the balance equation for the net momentum, we demonstrate that the perturbations may select two steady-state solitons from their continuous family existing in the absence of the dissipation and gain. In this case, the selected pulse with the lar ger value of the amplitude is expected to be stable, provided that the zero solution is stable. The prediction is completely confirmed by direct simul ations, If the integration domain is not very large, some pulses are stable even when the zero background is unstable, An explanation for the latter f inding is proposed. Furthermore, stable bound states of two and three pulse s are found numerically.