Excitation and interaction between solitons of the three-spine α-helical proteins under non-uniform conditions

Multi-soliton solutions of the three-coupled nonlinear Schrödinger equations, which describe the bioenergy transport mechanism in the three-spine α-helical protein, are analytically obtained by means of the similarity transformation. Based on these analytical solutions as initial values, the dynamical evolution of soliton is numerically discussed. Some new phenomena of soliton evolution are found in the time-varying parabolic external potential. The role of the parabolic external potential to influence soliton excitation is studied. The influence of propagation direction of the soliton increase with the add of the parabolic density. Moreover, the law of soliton motion and the distribution of the energy of the coupling equation are interpreted. These results have potential value for the propagation of bio-energy in the protein and nonlinear optics.