Long-range modulated wave patterns in certain nonlinear saturation alpha-helical proteins

We study the dynamic of modulated solitary wave patterns in alpha-helical proteins going beyond the standard nearest-neighbor interaction by taking into account influence of long-range dipole–dipole interactions of the power low type. In particular, self-trapping of amide-I energy quanta or exciton by the induced phonon deformation of the hydrogen-bonded lattice of peptide groups is capable of generating moving solitary waves following the Davydov soliton model. Under the adiabatic approximation, the discrete biexciton system is reduced to two coupled nonlinear Schrödinger equations where the dispersive coefficient depends on the long-range interactions parameter and the coupled term depends on the nonlinear saturation effects. We perform the linear stability analysis of continuous wave solutions of the coupled system. This analysis reveals that both nonlinear saturation and long-range interaction parameters affect the dispersion area. More new analytical multisoliton, bright and dark soliton solutions-like patterns are obtained using extended auxiliary equation method. We also observe the time behavior of modulating bright soliton-like pattern due to the nonlinear saturation and long-range interactions terms through numerical simulations.