The NuSTAR experiment detected a hard X-ray emission (10-70 keV) with a period of 8.68917 s and a pulse-phase modulation at 55 ks, or half this value, from the anomalous X-ray pulsar (AXP) 4U 0142+61. It is shown here that this evidence is naturally explained by the precession of a Keplerian supernova fallback disc surrounding this AXP. It is also found that the precession of discs formed around young neutron stars at distances larger than those considered in the past, may constitute almost neglected sources of gravitational waves with frequencies belonging to the sensitivity bands of the future space interferometers LISA, ALIA, DECIGO and BBO. In this work the gravitational wave emission from precessing fallback discs possibly formed around young pulsars such as Crab in a region extending beyond 8$times$10$^{7}$ m from the pulsar surface is estimated. It is also evaluated the role that infrared radiation emission from circumpulsar discs may play in contributing to Inverse Compton Scattering of TeV energy positrons and electrons. Extensive observational campaigns of disc formation around young and middle aged pulsars may also contribute to solve the long-standing problem of a pulsar origin for the excess of positrons in cosmic rays observed near Earth above 7 GeV. In the near future the James Webb telescope, with unprecedented near and mid-infrared observation capabilities, may provide direct evidence of a large sample of supernova fallback discs.
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