Stability of three-dimensional solitons in liquid films vertically flowing down

The stability of three-dimensional solitary waves in liquid films vertically flowing down is analyzed. The three-dimensional regimes in liquid films vertically flowing down are described by the system of equations for the layer thickness, the discharge rate in the gravity direction, and the discharge rate in the perpendicular direction. Localized perturbation in the active medium can be unstable with respect to the continuous spectrum. The plane-parallel flow far from the soliton hump is unstable, and if the three-dimensional soliton is considered as a source of localized noise, this noise forms an expanding unstable wave packet in space. It is stable with respect to the continuous spectrum, if the solitons moves faster or slower than the packet.