  Flexoelectric effect impact on the generalized susceptibility and soft
phonons dispersion was not studied in the long-range ordered phases of
ferroics. The gap in the knowledge motivated us to establish the impact of the
flexocoupling on the correlation function of the long-range order parameter
fluctuations in ferroelectric phase of ferroics with local disordering sources.
Within Landau-Ginzburg-Devonshire approach we obtained analytical expressions
for the generalized susceptibility and phonon dispersion relations in the
ferroelectric phase. Unexpectedly, the joint action of static and dynamic
flexoelectric effect induces non-diagonal components of generalized
susceptibility, which amplitude is proportional to the convolution of the
spontaneous polarization with flexocoupling constants. The flexocoupling
essentially broaden the k-spectrum of generalized susceptibility and so
decreases the correlation radii, as well as leads to the additional "pushing
away" of the optical and acoustic soft mode phonon branches. The contribution
of spontaneous polarization via ferroelectric nonlinearity and electrostriction
mechanisms can lead to both broadening and narrowing on the susceptibility
k-spectrum. Due to the joint action of flexoelectric coupling and spontaneous
polarization the degeneration of the transverse optic and acoustic modes
disappears in the soft phonon spectrum in a ferroelectric phase in comparison
with the spectra in a paraelectric phase. These effects have been studied
quantitatively for ferroelectric lead zirconate titanate using realistic values
of static and dynamic flexocouplings and cubic symmetry approximation for the
elastic properties. Also we derived general expressions for correlation
function for arbitrary symmetry, elastic and electrostrictive anisotropy.
