By H. D. Megaw

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**Additional info for Ferroelectricity In Crystals **

**Example text**

E. 36) If the nonlinearity parameter g = gO(1-S 2 )-1 depends on the velocity then the inertial of displacements of the peptide groups arises. 37), is an integral of motion. 1). 6), by the amound gO/~. 41) by the soliton. 4) then the soliton energy grows by increasing its degree of localization. In the limit g + 9~ 2 /4£ (when nO + QO)' the ratio of the soliton kinetic energy Es,k to the kinetic energy of the initial excitation Ek is given as follows 0 85 1+20Bg/3£ / Es,k Ek =. e. by the form of the initial wave function.

Aat +n ! 1) where m is an effective exciton mass, G : X2/K(1_s2) is a nonlinearity parameter. 1) in the standard form 2 ( i 3aT + 3ax 2 +2gl~(X,T) 12) ~(X,T): o. 3) This equation, for any nonvanishing positive value of g, and, therefore, for an arbitrary value of the coupling parameter X, has the normalized particular,solution of the form ~(X,T) where W : : 2 ~ g l exp[i(2kX-WT)]sech[g(x-4kT)/2], 2 4 (k -g /16), 2k : mav/h. 4) characterizes a solitary wave, or soliton, propagating along the ax-axis with a constant velocity v.

5. The dependence of the soliton and the exciton energies on their velocities: (1) the soliton energy; (2) the exciton energies; (3) the energy of metastable excitons; and (VO) the longitudinal sound velocity. words, their kinetic energy is not transformed into heat motion energy. This is the second important feature which provides their great stability in soft molecular chains. Finally, the third reason for the stability of the solitons considered is their topological stability. 5). Therefore, to the right of the soliton (~ > 0) all the peptide groups are in their undisplaced positions, na, and to the left (~ < 0) they are displaced by the same distance Thus, as n ~ 00, all the peptide groups occupy the positions na, and at n ~ _00, their positions are characterized by the following values na+S O' In order to annihilate the soliton it is necessary to return all the peptide groups on the left part of the chain to their initial positions na.

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