It has been known for a long time that when a liquid bath is vertically vibrated at a frequency f₀ with an acceleration larger than an onset value, the whole surface becomes unstable and a pattern of stationary waves of frequency f₀/2 forms spontaneously due to parametric forcing. This phenomenon was discovered by Faraday in 1831 [ref 1] and investigated more recently as a pattern forming instability [ref 2,3]. All the experiments on bouncing droplets are performed below the threshold [ref 4] of this instability so that in the absence of drop the interface is flat. As described in the previous section the regime of bouncing depends on the drop size and the forcing amplitude. As seen in film I.3 the vertical bouncing can become sub-harmonic so that the droplet collides with the surface only once in two periods of the forcing oscillation. This occurs for forcing amplitudes that are below but close to the Faraday instability threshold so that the droplet acts as an efficient local exciter of Faraday waves. The drop thus bounces on a surface affected by large amplitude waves and there is a spontaneous breaking of symmetry [P2-P4] by which the droplet starts moving horizontally on the interface. In this regime the bouncing droplet and the wave it generates remain phase-locked and the whole object, the drop and its associated wave, become spontaneously propagative. Fast camera recordings show that in this regime, at each bounce, the drop hits the forefront of the central bump of the wave created by the previous shocks (Film III.3). This impact on a locally slanted surface gives the drop a horizontal kick that will be repeated at the next period. On the average it results in a mean force, generating the motion. Because of nonlinear saturation, the droplet reaches a constant limit speed V_W that is of the order of 1/20th of the phase velocity V_f of the surface waves.

We called "walker" [P2, P3, P4] the coherent object formed by the association of the droplet and the wave-field it generates [ref 5-8]. In spite of the system being dissipative, this self-propagative structure is sustained. The bath oscillation provides energy both to the drop (to maintain its bouncing) and to the waves (through their parametric forcing). It is a symbiotic association: if the drop coalesces with the bath, the wave vanishes. Inversely, if the waves are damped (for example in regions where the liquid layer is thin), the drop stops travelling.