Collective modes in uniaxial incommensurate-commensurate systems with a real order parameter

The basic Landau model for uniaxial systems of class II is non-integrable, and allows for various stable and metastable periodic configurations, beside that representing the uniform (or dimerized) ordering. In the present paper we complete the analysis of this model by performing the second-order variational procedure, and formulating the combined Floquet-Bloch approach to the ensuing non-standard linear eigenvalue problem. This approach enables an analytic derivation of some general conclusions on the stability of particular states, and on the nature of accompanied collective excitations. Furthermore, we calculate numerically the spectra of collective modes for all states participating in the phase diagram, and analyse critical properties of Goldstone modes at all second- and first-order transitions between disordered, uniform and periodic states. In particular, it is shown that the Goldstone mode softens as the underlying soliton lattice becomes more and more dilute.