The conditions governing the motion of a screw dislocation at velocities above and below the velocity of shear waves are contrasted. For supersonic motion the Peierls-Nabarro equation becomes a differential equation, in contrast to the subsonic integral equation. It has a solution representing a moving restoration of fit along a slip plane across which there was originally complete misfit. In a dispersive medium where the sound velocity decreases with decreasing wavelength a dislocation moving between the maximum and minimum sound velocities suffers a retarding force, which may be calculated if the shape of the dislocation is supposed to be known.
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J. D. Eshelby (1956) studied this question.
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