  We consider the Davydov model of {\alpha}-helix protein chain with both
exciton-exciton and excitonphonon couplings and investigate on the evolution of
elliptic solitons. In the discrete regime of the adiabatic limit, we
analytically and numerically show that modulational instability induces the
self-localization of energy in the {\alpha}-helix protein chain. By
incorporating the continuous limit approximations, various nonlinear periodic
modes are traced; strongly suggesting that the energy of the ATP hydrolysis is
locally distributed over the {\alpha}-helix protein chain. It is generally
found that the exciton-exciton coupling induces the inhomogeneity in the
protein chain, which greatly enhances energy localization that is physically
manifested as nonlinear periodic modes. Results of numerical simulations
clearly depicts the evolution of these nonlinear periodic modes in the highly
discrete, nonlinear, and coupled system that governs the dynamics of
{\alpha}-helix protein chain.
