Photometric observations of the cataclysmic variable EQ?Lyn (SDSS?J074531.92+453829.6), acquired from 2005 October to 2006 January, revealed high-amplitude variability in the range 1166-1290?s. This accreting white dwarf underwent an outburst in 2006 October, during which its brightness increased by at least five magnitudes, and it started exhibiting superhumps in its light curve. Upon cooling to quiescence, the superhumps disappeared and it displayed the same periods in 2010 February as prior to the outburst within the uncertainties of a couple of seconds. This behavior suggests that the observed variability is likely due to nonradial pulsations in the white dwarf star, whose core structure has not been significantly affected by the outburst. The enigmatic observations begin with an absence of pulsational variability during a multi-site campaign conducted in 2011 January-February without any evidence of a new outburst; the light curve is instead dominated by superhumps with periods in the range of 83-87?minutes. Ultraviolet Hubble Space Telescope time-series spectroscopy acquired in 2011 March reveals an effective temperature of 15,400?K, placing EQ?Lyn within the broad instability strip of 10,500-16,000?K for accreting pulsators. The ultraviolet light curve with 90% flux from the white dwarf shows no evidence of any pulsations. Optical photometry acquired during 2011 and Spring 2012 continues to reflect the presence of superhumps and an absence of pulsations. Subsequent observations acquired in 2012 December and 2013 January finally indicate the disappearance of superhumps and the return of pulsational variability with similar periods as previous data. However, our most recent data from 2013 March to May reveal superhumps yet again with no sign of pulsations. We speculate that this enigmatic post-outburst behavior of the frequent disappearance of pulsational variability in EQ?Lyn is caused either by heating the white dwarf beyond the instability strip due to an elevated accretion rate, disrupting pulsations associated with the He II instability strip by lowering the He abundance of the convection zone, free geometric precession of the entire system, or appearing and disappearing disk pulsations.
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