Geodesic
Nonlinear orientational dynamics of a~molecular chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 227-244

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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.
Keywords: nonlinear dynamics, nonlinear oscillation, nonlinear wave, molecular crystal
Mots-clés : phonon, normal mode, sine-Gordon equation, solid–liquid transition. 
@article{TMF_2011_168_2_a3,
     author = {V. A. Lykakh and E. S. Syrkin},
     title = {Nonlinear orientational dynamics of a~molecular chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {227--244},
     publisher = {mathdoc},
     volume = {168},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a3/}
}
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V. A. Lykakh; E. S. Syrkin. Nonlinear orientational dynamics of a~molecular chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 2, pp. 227-244. http://geodesic.mathdoc.fr/item/TMF_2011_168_2_a3/