We present the results of TRIFFID simultaneous V- and B-band observations of the cores of the globular clusters M15, M92 and NGC 6712. A variability search of their dense centres was made feasible through performing post-exposure image sharpening on the images, increasing the image resolution by a factor of ~2. The ISIS implementation of the image subtraction technique developed by Alard & Lupton was then used to detect flux variations in our image sets. We have obtained periods for all observable variables (in our field of view) in NGC 6712 and we have found two new RR Lyrae variables (an RRab and an RRc). We have confirmed three variables in our field of view of the M92. For M15, we detect 48 variables in our field of view, 23 of which are new discoveries. We obtain periods and amplitudes for all variables and classify new ones based on the light-curve shape, the most significant period and the mean magnitude in the V band. Among the detected RR Lyrae we find 19 RRc, 12 RRab and two RRd types. In the subsequent analysis we find a marked increase in RRc over RRab variables in the core. In a refined procedure to search for fainter objects we find no dwarf novae in our field of view of M15. Simulations performed on the data set to quantify our sensitivity to such objects indicate that an upper limit of 10 dwarf novae (at 92 per cent probability) exist in our field of view. The implications this result has on globular clusters are discussed.