Simulation of moderately long nonlinear spatial waves on the interface between two fluid flows in a horizontal channel

► A new model that consists of one basic and several auxiliary equations is proposed. ► Nonlinear spatial interface waves can simultaneously propagate at arbitrary angles. ► Transformations of perturbations and their various interactions were investigated. ► An effect of the stationary two-layered shear flow on perturbations was determined. ► Plane solitary waves of the different polarity can travel in the opposite directions.