On the motion of solitons in discrete molecular chains

A perturbation theory for solitons is developed using the Ablowitz–Ladik equation as unperturbed equation. The soliton dynamics in a discrete molecular chain is studied in the framework of this theory. It is shown that the motion of the center of mass of the soliton is equivalent to the motion of a certain effective particle in a periodic potential with period equal to the lattice constant. Criteria for finite and infinite motions are found. The frequency of oscillations of the soliton in the potential well is calculated. The correction to the soliton mass associated with allowance for the discrete nature of the chain is found.