Analytical study on the generalized Davydov model in the alpha helical proteins

In this paper, we investigate the dynamics of a generalized Davydov model derived from an infinite chain of alpha helical protein molecules which contain three hydrogen bonding spines running almost parallel to the helical axis. Through the introduction of the auxiliary function, the bilinear form, one-, two- and three-soliton solutions for the generalized Davydov model are obtained firstly. Propagation and interactions of solitons have been investigated analytically and graphically. The amplitude of the soliton is only related to the complex parameter mu and real parameter theta with a range of [0, 2 pi]. The velocity of the soliton is only related to the complex parameter mu, real parameter theta, lattice parameter epsilon, and physical parameters beta(4), beta(3) and beta(4). Overtaking and head-on interactions of two and three solitons are presented. The common in the interactions of three solitons is the directions of the solitons change after the interactions. The soliton derived in this paper is expected to have potential applications in the alpha helical proteins.