Breather bright solitary waves generation induced by lattice deformations and electron–peptide asymmetry interaction degree in a generalized Davydov–Scott model for polarons in linear peptide chains

Polarons are quasiparticles whose properties are well known to influence important properties of material and nowadays, are expected to affect the dynamics of biomolecules. Elaborating on a recently introduced generalized model of linear polypeptides chains like the \(\alpha \)-helical chains of proteins, the generation and emergence of breather bright solitary waves is analyzed via the modulation instability mechanism. It is shown that important features of the model, the right lattice deformations, and the degree of spatial asymmetry of the electron–peptide interactions profoundly alter the instability and the emergence of breather bright solitary waves. Analytical predictions of modulation instability are corroborated by intensive numerical simulations. Right lattice deformations favor the instability and the emergence of breather bright solitary waves, while the degree of spatial asymmetry of the electron–peptide interaction softens the instability. The lifetime of bright solitary waves generated in this work being within experimental range suggests that they are good candidates to explain transport and energy localization of amide-I excitations for example.