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We consider the tunneling motion of protons within a hydrogen bonded (HB) chain. Each proton is subjected to a coulomb interaction from the nearest heavy ions, as well as from the two neighboring protons. We investigate the nonlinear proton dynamics of a HB chain in the semiclassical limit using the coherent state method combined with the Holstein–Primakoff bosonic representation. The protonic transport mechanism has arisen due to the neighboring proton–proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We construct the exact periodic solutions in terms of elliptic functions by invoking a discrete Jacobian elliptic function method. We present a detailed analysis of the effect of the interaction strength of neighboring protons in the process of bioenergy localization in the form of coherent localized breather modes in a discrete HB chain. A linear stability analysis is performed and the eigenvalues are strictly lying in the imaginary axis, confirming the stable nature of the obtained solutions.

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