B757 reported encountering either severe turbulence or wake from the preceding A319 departing EWR.

Narrative

EWR was using [a] single runway for arrivals and departures due to runway construction. The aircraft departing prior to us was an Airbus A319. We were cleared for takeoff and departed [Runway] 4R for a normal departure. Upon reaching 500 ft AGL we experienced our first buffet which didn't seem abnormal due to gusty winds reported in the area. Once crossing about 1000-1500 ft the buffeting became violent. It varied in intensity but increased to the point that I was coming off my seat; couldn't read the flight instruments; and it knocked my headset off. The buffeting seemed to be cyclical and almost mechanical in nature. It seemed very similar to wake turbulence but lacked any roll moment. My initial thought was that it was wake turbulence but didn't think we were close enough to the aircraft ahead for that type of a wake encounter. I varied my rate of climb to see if I could escape what I thought was a wake. The turbulence continued for maybe 30 seconds and eventually stopped passing through about 4000 ft. We continued to climb and cleaned up the aircraft and reported to ATC about the turbulence. I had the First Officer call back to check on the flight attendants. To be honest I still am not sure if it was wake or severe turbulence. It was the most violent encounter I have experienced in years.