Incommensurate phases in systems with coupling between acoustic and optic modes

Incommensurability in crystals may occur in case of frustration. This creates possibly an instability. The situation is more complicated in case the instability occurs in a phonon branch that is coupled to another one. Examples of such cases are discussed. The lattice dynamics in the incommensurate phase as well as in the prototype and the low-temperature phase are studied. The model involves besides frustration also nonlinear interactions, and is especially useful for the family of compounds with Pnma symmetry.