Existence of Dynamic Phase Transitions in a One-Dimensional Lattice Model with Piecewise Quadratic Interaction Potential

The existence of travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two stable phases. We develop a framework such that the existence of subsonic heteroclinic waves in a bi-infinite chain of atoms can be proved rigorously. The key is to represent the solution as a sum of a (here explicitly given) profile and a corrector in $L^2(\mathbb{R})$. It is demonstrated that the kinetic relation can be easily inferred from this framework.