For the problem of the dynamics of weakly nonlinear three-dimensional perturbations of two shallow liquid layers in a horizontal channel in the presence of steady shear flow, a combined model is obtained, which consists of one main nonlinear evolution equation and several simple auxiliary linear equations. The latter are necessary to find the vectors of horizontal velocities of the liquid and other quantities appearing only in terms of second order of smallness of the main equation. Use of the constructed model made it possible to study different types of interaction between the localized perturbations. In particular, it is demonstrated that plane or quasi-plane solitary waves of different polarity are able to propagate simultaneously along the interface shear flow. It is also shown that a weakening of disturbances moving in the direction of flow, and conversely, and strengthening of waves traveling against the flow may be observed.
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