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The amide-I [Formula: see text] -helix protein is a long molecular chain made up of regularly spaced peptide groups interacting via C=O bonds. According to the current theory the energy released by hydrolyzed adenosine triphosphate is carried across the protein via vibration modes, caused by C=O bond stretchings which, in the presence of anharmonic molecular vibrations, can promote nonlinear localized excitations called excitons. In this work the effects of long-range interactions between amide-I molecules on the modulational instability of small-amplitude excitons, and on characteristic parameters of soliton wavetrain-type excitons, are investigated with emphasis on long-range interactions saturating at finite intermolecular interaction ranges. It is found that long-range interactions strongly affect the dispersion of vibration modes of the protein chain, causing a narrowing of the modulational-instability regions for small-amplitude excitons. Characteristic parameters of the exciton soliton wavetrain, including its velocity, tail and average width (i.e., the exciton width at half tail), are drastically enhanced with respect to their values when only the short-range interaction is considered. The results suggest a sizable increase of the energy carried by excitons along the protein chain above predictions based on short-range considerations.

Exciton–polariton solitons are nonlinear quasiparticles composed of exciton–photon bound states due to the interaction of light with matter. In semiconductor micro-cavity systems, such as semiconductor micro and nanowires, polaritons are characterized by a negative mass which, combined with the repulsive nonlinear exciton–exciton interaction, leads to the generation of bright polariton solitons. In this work, we investigate the dynamics of bright exciton–polariton solitons in a finite-sized microcavity waveguide, assuming radiative losses to be balanced by the external pumping. Bright-soliton solutions to the model equations of motion, which consist of a periodic train of polariton pulses, are obtained in terms of Jacobi elliptic functions. Analytical expressions of the energies of both photonic and excitonic components of the pulse train are found. Results suggest that the size of a nanowire waveguide plays a relevant role in the quantitative estimate of the energy conveyed by polariton solitons propagating in the medium.

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