Self-Trapping in a Molecular Chain with Substrate Potential

Abstract

We introduce here an improved version of the well known Davydov model for α-helix proteins and other hydrogen-bonded molecular chains, where the coupling of the chain with its atomic environment is taken into account via the introduction of an on-site harmonic potential for each molecule. For some standard sets of values for the physical parameters, the self-trapping mechanism occurs and two-component soliton excitations are generated in the molecular chain. The first component is the well known pulse excitonic (or electronic) soliton while the second component for the molecular vibrations is quite different. Due to the one-minimum on-site potential the vibrational component becomes a localized wave with zero asymptotic values. In the contrary of the initial Davydov model low energy exciton periodic solutions are also possible in this model. Both solitons and excitons are obtained here using a steepest descent numerical minimization technique. Their dynamics and stability are studied by numerical simulations of the discrete initial equations.