The paper's primary goal and scientific contribution is the mathematical simulation of nonlinear surface waves in moving thin layers of perfect liquids with accounting for the combined influence of mass sources and surface activity at the free-moving boundaries. The original inverse numerical method has been developed and implemented in a computer code. The main results of the work lie in establishing certain conditions when, under the weak intensity of the bottom sources and free surface activity, the propagation of solitary waves with slowly changing characteristics and surface ripple is possible. The estimate of orders of the main control parameters in the mathematical model was also given. For selected sets of control parameters, computer simulation has been carried out, and the shapes of the surface of propagating nonlinear waves have been calculated. It was established the amplitude of the carrier wave increased 1.5 times by the joint influence of the weak mass source and surface activity at the moving boundary. In addition, the ripple intensity increased significantly, accounting for surface activity.