  More than two dozen soft gamma-ray repeaters (SGRs) and anomalous X-ray
pulsars (AXPs) have been detected so far. These are isolated compact objects.
Many of them are either found to be associated with supernova remnants or their
surface magnetic fields are directly measured, confirming that they are neutron
stars (NSs). However, it has been argued that some SGRs and AXPs are highly
magnetized white dwarfs (WDs). Meanwhile, the existence of super-Chandrasekhar
WDs has remained to be a puzzle. However, not even a single such massive WD has
been observed directly. Moreover, some WD pulsars are detected in
electromagnetic surveys and some of their masses are still not confirmed. Here
we calculate the signal-to-noise ratio for all these objects, considering
different magnetic field configurations and thereby estimate the required time
for their detection by various gravitational wave (GW) detectors. For SGRs and
AXPs, we show that, if these are NSs, they can hardly be detected by any of the
GW detectors, while if they are WDs, Big Bang Observer (BBO), DECi-hertz
Interferometer Gravitational wave Observatory (DECIGO) and Advanced Laser
Interferometer Antenna (ALIA) would be able to detect them within a few days to
a year of integration, depending on the magnetic field strength and its
configuration. Similarly, if a super-Chandrasekhar WD has a dominant toroidal
field, we show that even Laser Interferometer Space Antenna (LISA) and TianQin
would be able to detect it within one year of integration. We also discuss how
GWs can confirm the masses of the WD pulsars.
