We analyse a model of the fluid flow between elastic walls simulating arteries actively interacting with the blood. The lubrication theory for the flow is coupled with the pressure and shear stress from the walls. The resulting nonlinear partial differential equation describes the displacement of the walls as a function of the distance along the flow and time. The equation is solved numerically using the one-dimensional integrated radial basis function network (1D-IRBFN) method. Solutions in the form of self-sustained trains of pulses are explored. Numerical experiments demonstrate the process of formation of the pulses from randomly chosen initial conditions.