Radiation of Langmuir solitons

It is shown that a Langmuir soliton radiates a resonant wave with the phase velocity equal to the soliton velocity. The group velocity of the radiated wave is less than the soliton velocity and, therefore, the soliton radiates backward. The amplitude of the radiated wave is calculated analytically with asymptotic accuracy in the limiting case of small soliton amplitudes. Soliton attenuation and slowing down, caused by the radiation, are also calculated.