The motion of an excess electron or intramolecular dipole excitation interacting with local deformation in a molecular chain is investigated with the fourth spatial derivative term in the continuum limit and anharmonicity taken into account. The existence of the two types of bell-shaped solitons is established. The first type solitons can travel with both subsonic and supersonic velocities while the second type ones only with velocities exceeding that of the longitudinal sound in the chain.
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Davydov et al. (1984) studied this question.
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