Inhomogeneous configurations in the Lifshitz-type improper incommensurate ferroelectric thin films

The model with the Lifshitz invariant for periodic and helicoidal structures has been analyzed without neglecting of the amplitude function oscillations considering the amplitude and phase functions as equal in significance variables. We have shown that this approach gives significantly richer picture of the order parameter phase and amplitude distribution, than in the approximation of the constant amplitude. The amplitude function oscillations are shown to be extremely important for finding of the phase function distribution in a thin film. Along with numerical calculations, analytic consideration is carried out in the limit of small anisotropy. Both regular and chaotic regimes are studied.