Radiation of Sound Waves Via Soliton Excitation of the Angarmonic Chain of Atoms in a Dislocation Core

It is demonstrated that propagation of the soliton described by the Boussinesq equation along a linear defect of the crystal structure leads to radiation of sound waves (analog of the Vavilov–Cherenkov effect). Radiation that has a continuous spectrum diverges conically from the dislocation line, and the apex angle of the cone is determined by the ratio of the sound speed in the crystal to the soliton speed. With increasing soliton speed, the maximum of the spectral flux density of sound energy is displaced toward higher frequencies. An analytical expression for energy losses is derived.