Nonlinear orientational dynamics of a molecular chain. (English. Russian original) Zbl 1274.82068

Lykakh, V. A.; Syrkin, E. S.

Theor. Math. Phys. 168, No. 2, 1048-1063 (2011); translation from Teor. Mat. Fiz. 168, No. 2, 227-244 (2011).

Summary: We investigate the nonlinear rotational dynamics of a molecular chain with quadrupole interaction in both the discrete and the continuous cases. Based on a system of nonlinear differential-difference equations, we obtain approximate equations describing the chain excitations and preserving the initial symmetry. We introduce an effective potential and normal coordinates, using which allows decoupling the system into linear and nonlinear parts. As a result of a strong anisotropy of the potential, narrow “valleys” occur in the angle plane. Motion along a valley corresponds to a softer interaction (nonlinear equations). Linear equations describe motion across a valley (hard interaction). We consider cases where the derived nonlinear equations reduce to the sine-Gordon equation. We find integrals of motion and exact solutions of our approximate equations. We uniformly describe the energy interval encompassing the domains of order, of orientational melting, and of rotational motion of the molecules in the chain.

MSC:

82D25	Statistical mechanics of crystals
35Q55	NLS equations (nonlinear Schrödinger equations)

Keywords:

nonlinear dynamics; nonlinear oscillation; nonlinear wave; molecular crystal; phonon; normal mode; sine-Gordon equation; solid-liquid transition

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