A tale of three cataclysmic variables with distinct superhumps

Superhumps are among the most commonly observed variable features in the light curves of cataclysmic variables (CVs). To study the superhump behaviour of CVs, we present Transiting Exoplanet Survey Satellite (TESS) observations of three CVs: CRTS J110014.7+131552, SDSS J093537.46+161950.8, and PK2008 HalphaJ130559. Among them, a super-outburst has been observed in CRTS J110014.7+131552, which is associated with the precursor outburst, where prominent superhumps have been observed during maximum of the outburst with a mean period of 0.06786(1) d. We observed variations in the superhump period, along with changes in the shape of the light curve profile and the amplitude of the superhumps during different phases of the outburst, indicating disc-radius variation as well as periodically variable dissipation at the accretion stream's bright spot. The data on SDSS J093537.46+161950.8 reveal previously unknown variations modulated with periods of 0.06584(2) d and 2.36(2) d, related to the positive superhump and the disc-precession periods, respectively, which can reasonably be interpreted as a result of the prograde precession of an eccentric accretion disc. Despite its short orbital period, the lack of outburst activity, its stable long-term brightness, discovery spectrum, and absolute magnitude suggest that the object might not be an SU UMa type dwarf nova. Instead, it could belong to the group of high-mass-transfer CVs below the period gap: either a rare class of nova-like variables or a high-luminosity intermediate polar, a subclass of magnetic CVs. For PK2008 HalphaJ130559, a new average orbital period of 0.15092(1) d has been identified. Additionally, this system displays previously undetected average periods of 0.14517(3) d and 3.83(1) d, which could be provisionally identified as negative superhump and disc-precession periods, respectively. If the identified simultaneous signals do indeed reflect negative superhump and disc-precession period variations, then their origin might be associated with the retrograde precession of a tilted disc and its interaction with the secondary stream.