  Highly energetic astrophysical phenomena like supermassive black hole binary
(SMBHB) mergers are predicted to emit prodigious amounts of gravitational waves
(GWs). An anticipated component of the gravitational waveform known as "memory"
is permanent and non-oscillatory. For SMBHB mergers, the memory is created
primarily during the most violent moments of the inspiral immediately preceding
the final plunge and ring-down when the strongest gravitational fields are at
work and the non-linearities of general relativity are most pronounced. The
essentially time-domain nature of memory makes it forbiddingly difficult to
detect with ground based GW detectors, leaving pulsar timing array (PTA)
experiments as the most promising means by which it may be detected and
studied. In this paper, we discuss how GW bursts with memory (BWMs) influence
pulsar timing experiments and develop methods to assess how sensitive modern
timing efforts are to such GW events. We discuss how PTA searches for BWMs can
be used to constrain the rate of BWMs and how these constraints relate to
information regarding the population of SMBHBs.
