“Relativistic” characterisation of the energy of soliton-like defects in continuous media

The foundation of the relativistic behaviour of some classical physical models is investigated. It is shown that, in the case of moving screw dislocations as well as in the continuum Frenkel–Kontorova model (Sine-Gordon equation and generalisations), the value of a particular function associated with the static equilibrium solutions plays a fundamental role in obtaining a fully relativistic behaviour of the energy. Finally, the equivalence between mass and energy and the presence of preferred frames of reference are considered.