In each season when the DA pulsating white dwarf G29–38 has been observed, its period spectrum appears very different, but it always contains a forest of harmonics and cross-frequencies. The ratio of the amplitude of these non-linear frequencies Ac to the product of the amplitudes of the corresponding parent modes A1A2 has been measured. The results are compared with the predictions given by three existing theoretical models. Our analysis shows that the non-linear frequencies present in the period spectrum of G29–38 owe their presence mostly to the inelastic response of the stellar medium to the perturbation travelling through it, rather than to the non-linear response of the emergent luminous flux to the surface temperature variation. This analysis also confirms that most identified modes are ℓ=1, as previously asserted by Kleinman et al.