We have studied analytically and numerically a nonlinear diatomic lattice with a cubic nearest-neighbor interaction potential. Our system is a one-dimensional chain of pairs of atoms interacting through a ''hard'' interaction, each pair being bound to the neighboring pairs by a ''soft'' interaction. This is a simple model for hydrogen-bonded molecular chains, like the spines in an alpha helix. We have used a multiple-scale reductive perturbative technique to transform the equations of motion, and derived a nonlinear Schrodinger equation describing the time evolution of localized solitonic excitations. We have also derived analytically, following the method introduced by Zakharov and Shabat, the thresholds for the creation of solitons when the chain is initially excited by a square wave, which is a model of a generic localized excitation. We have performed afterwards several molecular-dynamics simulations at zero temperature. We have found that localized solitonlike excitations can propagate along the chain without being significantly altered; if the initial excitation has a square-wave shape, it evolves into a solitonlike excitation also traveling along the chain. However, if the initial excitation is excessively broad it tends to disperse in a way similar to a linear system; on the other hand, if the excitation is too narrow it may become pinned at the initial position. Finally, we have repeated our simulations in presence of thermal disorder corresponding to temperatures ranging up to 300 K. We have found that the thermal vibrations not only do not destroy the solitonlike excitations, but do not even alter in any significant way their propagation along the molecular chain.
Campa, A., Giansanti, A., Tenenbaum, A., Levi, D., Ragnisco, O. (1993). QUASISOLITONS ON A DIATOMIC CHAIN AT ROOM-TEMPERATURE. PHYSICAL REVIEW. B, CONDENSED MATTER, 48(14), 10168-10182 [10.1103/PhysRevB.48.10168].