Because soft mode moves to this "central peak" that takes constant position.
Among the early (maybe earliest?) papers that discussed the central peak were inelastic neutron scattering experiments on SrTiO3, studying its structural phase transition near 100 K. Here are some references:
Riste, et al, Solid State Commun, 9, 1455 (1975)
Shapiro, Axe, Shirane, Riste, Phys Rev B 6, 4332 (1972)
Axe, Shapiro, Shirane, Riste, in Anharmonic Lattices, Structural Phase Transitions & Meilting (Noordhoof, Groningen, 1974), p. 23.
The central peak (a strong peak in the spectrum centered on zero frequency) and the "soft mode" peak are coexisting features in the spectrum. The central peak has been attributed to propagation of nonlinear waves (solitons) in the crystal, in distinction to the linear phonons, of which the soft mode is one. I am the author of a couple of the papers on this problem:
Kerr, Phys Rev B 19, 5773 (1979);
Kerr, Baeriswyl, Bishop, PRB 24, 6566 (1981).
The centre of the peak corresponds to zero frequency shift in scattering spectrum in contract to stokes and antistokes components which are shifted on the phonon frequency in opposite directions.
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