  The standard technique for very low-frequency gravitational wave detection is
mainly based on searching for a specific spatial correlation in the variation
of the times of arrival of the radio pulses emitted by millisecond pulsars with
respect to a timing model. This spatial correlation, which in the case of the
gravitational wave background must have the form described by the Hellings and
Downs function, has not yet been observed. Therefore, despite the numerous
hints of a common red noise in the timing residuals of many millisecond pulsars
compatible with that expected for the gravitational wave background, its
detection has not yet been achieved. By now, the reason is not completely clear
and, from some recent works, the urgency to adopt new detection techniques,
possibly complementary to the standard one, is emerging clearly. Of course,
this demand also applies to the detection of continuous gravitational waves
emitted by supermassive black hole binaries populating the Universe. In the
latter case, important information could, in principle, emerge from the
millisecond pulsars considered individually in a single-pulsar search of
continuous GWs. In this context, the surfing effect can then be exploited,
helping to select the best pulsars to carry out such analysis. This paper aims
to clarify when the surfing effect occurs and describe it exhaustively. A
possible application to the case of the supermassive black hole binary
candidate PKS 2131-021 and millisecond pulsar J2145-0750 is also analyzed.
