BOOSTED KINK-TYPE SOLITARY WAVES IN NONLINEAR ELASTIC MEDIA

After reviewing systems with scalar order parameters described by classical field theories with (i) static and boosted kinks in a conservative phi(4) system, and (ii) kinks propagating at only one allowed velocity in damped phi(6) systems, similar analysis is attempted for nonlinear elastic media. Static and boosted solitary wave solutions for the nonlinear (phi(4)) elastic problem are obtained, the latter of which has infinite energy, and corresponds to a traveling solitary wave obtained from a non-Lorentz length contraction. For damped systems with on-site potentials with local minima of unequal energy, it is shown that while propagating kinks are allowed in the scalar order parameter system, only in the (unphysical) overdamped limit can one find such excitations in the nonlinear elastic problem, unless strains at the boundary are chosen which are not local minima. The relevance of these results to the study of moving interfaces in nucleation and growth in first-order phase transformations is discussed.