A nondegenerate four-wave mixing (FWM) on a new type of Kerr nonlinearity determined by the layer deformations in smectic A liquid crystal (SmA) is considered. It is shown that in the case when the frequency difference of the coupled electromagnetic waves (EMW) is close to the frequency of the second sound (SS), a strong parametric coupling among EMW through the dynamic grating of layer deformations occurs. As a result EMW with the lowest frequency is amplified and EMW with the highest frequency is depleted, while the two EMW with the intermediate frequencies are compressed in space and their envelopes take the form of a spatial soliton. The explicit expressions of all amplitudes are calculated. The gain coefficient appears to be one order of magnitude greater than the one for stimulated scattering on an ordinary sound in organic liquids. The interaction of EMW with the specially selected frequencies and wave vectors gives rise to the analog of Brillouin enhanced FWM (BEFWM) resulting in the amplification of the phase-conjugate EMW. The additional components of the fundamental EMW and a spectrum of spatially localized Brillouin-like small harmonics with combination frequencies and wave vectors are generated due to the combined effect of the new kind of Kerr nonlinearity discussed and anisotropy of SmA. It is shown that the light generates spatially periodic hydrodynamic flow with the large-scab soliton-type envelopes. The light-induced layer deformations generate the high-frequency longitudinal electric field due to the flexoelectric effect. The spatial and temporal characteristics of the dynamic grating appears to be close to the experimental data.