  A model consisting of a mixed Kuramoto - Sivashinsky - KdV 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,
opening way to the existence of stable solitary pulses (SPs). Treating the
dissipation and instability-generating gain in the model as small
perturbations, we demonstrate that balance between them selects two
steady-state solitons from their continuous family existing in the absence of
the dissipation and gain. The may 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. Stable bound states of two and three pulses are found
too. The work was supported, in a part, by a joint grant from the Israeli
Minsitry of Science and Technology and Japan Society for Promotion of Science.
