  Pulsars are the fast rotating neutron stars with strong magnetic field, that
emit over a wide frequency range. In spite of the efforts during 40 years after
the discovery of pulsars, the mechanism of their radio emission remains to be
unknown so far. We propose a new approach to solving this problem for a subset
of pulsars with a high-frequency cutoff of the spectrum from the Pushchino
catalogue (the "Pushchino" sample). We provide a theoretical explanation of the
observed dependence of the high-frequency cutoff from the pulsar period. The
dependence of the cutoff position from the magnetic field is predicted. This
explanation is based on a new mechanism for electron radio emission in pulsars.
Namely, radiation occurs in the inner (polar) gap, when electrons are
accelerated in the electric field that is increasing from zero level at the
star surface. In this case acceleration of electrons passes through a maximum
and goes to zero when the electron velocity approaches the speed of light. All
the radiated power is located within the radio frequency band. The averaging of
intensity radiation over the polar cap, with some natural assumptions of the
coherence of the radiation, leads to the observed spectra. It also leads to an
acceptable estimate of the power of radio emission.
