Two exciton energy transfer in an inhomogeneous alpha-helical protein chain

In this paper, we study the two exciton energy transfer in an inhomogeneous alpha-helical protein chain by proposing a suitable model Hamiltonian. We build the theory of envelope solitons for this system based on the two trial functions proposed by Davydov after suitably modifying them for two exciton states. The underlying dynamics is investigated by constructing Lagrange's equation of motion which is found to be a perturbed nonlinear Schrödinger (NLS) equation. The effect of nonlinear inhomogeneity in the form of modified exchange interaction between sites is studied in terms of a soliton under perturbation. The perturbed soliton is constructed using a sine-cosine method. It is found that the presence of inhomogeneity causes soliton splitting and hence a disorder in the protein molecular system.