A stabilized Kuramoto-Sivashinsky system

A model consisting of a mixed Kuramoto Sivashinsky Korteweg de Vries equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra equation makes its possible to stabilize the zero solution in the model, thus opening way to the existence of stable solitary pulses (SPs). By means of the perturbation theory, treating dissipation and instability-generating gain in the model (but not the linear coupling between the 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 larger value of the amplitude is expected to be stable, provided that the zero solution is stable. The prediction is completely confirmed by direct simulations. If the integration domain is not very large, some pulses are stable even when the zero background is unstable. An explanation to the latter finding is proposed. Furthermore, stable bound states of two and three pulses are found numerically. PACS: 05.45.Yv, 46.15.Ff