Classical mechanical analogs of relativistic effects

The analogs of relativistic effects in classical mechanics, which are observed in the propagation of solitons in solids, are discussed. These effects are described by formulas similar to those of the special theory of relativity, with the speed of sound entering them in lieu of the speed of light. These parallels are shown to be a part of the correspondence between the soliton theory and field theories (in particular, electrodynamics). The effect of Lorentz-invariance breakdown in mechanical systems on dynamic soliton properties is considered. It is shown that supersonic solitons (in particular, dislocations) can propagate in such systems.