Interaction of acoustic and optical branches via a Lifshitz-type invariant

It is shown that the interaction of the acoustic and soft optical branches of the spectrum of normal vibrations of a crystal via a gradient invariant of the Lifshitz-invariant type explains the characteristic temperature dependences of these branches as the point of a transition from the initial phase into an incommensurate phase is approached. A comparison is made with the experimental data for betaine calcium chloride dihydrate — BCCD. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 707–710 (10 May 1997)