Nonlinear dynamics for proper ferroelastic transitions for which the landau condition is violated

On the basis of a lattice model the domain structure for ferroelastic transformations is examined. The model accounts for both strongly nonlinear and competing interactions which allow for, in some situations, the propagation of nonlinear excitations. The model can be mostly applied to proper ferroelastic transformations of which In-Tl, Ti-Ni, etc.… are good prototypes. The phonon dispersion of the transverse acoustic waves obtained in the linearized case is discussed and the results show first a phonon softening at nonzero wave-number and next an upwards convexity of the phonon branch near the long-wavelength limit. This can be seen as pre-transitional effects. In a fully nonlinear case we consider vanishing dilatation transformations and the continuum approximation is applied to the one-dimensional version. Then, we investigate nonlinear excitations; three main classes of solution are found: i) quasi-harmonic solutions corresponding to periodically modulated structures in space which is a precursor effect of the elastic transformation, ii) an array of solitons made of periodic arrangements of parent-elastic domains and iii) a moving strain soliton. All the significant results are numerically illustrated by means of the microscopic model. Finally, the similarity to martensitic transformations and some extensions of the model are outlined.