One-dimensional dislocations IV. Dynamics

Tho equations of motion of the one-dimensional dislocation model are studied, and all solutions representing disturbances propagated without change of form are obtained. These comprise: (i) dislocations, and regular sequences of the same, either of like or of alternating sign, travelling with velocity less than c, the characteristic wave velocity of the system; (ii) an iddislocations, and sequences of the spme, travelling with velocity greater than c; and (iii) waves of infinitesimal amplitude, belonging to two branches travelling respectively with velocities less than and greater than c. Only dislocations or sequences of dislocations of like sign, and waves of velocity less than c, correspond to stable equilibria. The dislocations exhibit ‘relativistic’ behaviour. The relevance of anti-dislocations to very fast slip in solids is considered, and rejected.