Alternate way of soliton solutions in hydrogen-bonded chain

Abstract

The transport of energy and charge along one-dimensional chains of hydrogen bonds is an extremely important problem in bioenergetic and solid-state situations. We present an alternate way to investigate the proton dynamics in a symmetric double-well potential created by the potentials of two heavy ions in a long periodic chains of hydrogen bonds forming the channels for proton transport. We formulate the Hamiltonian by incorporating quartic anharmonic proton–proton interaction. We invoke the modified extended tangent hyperbolic method (METF) embedded with symbolic computation to solve the associated two coupled equations of motion. We propose a series of new forms of the potential relief of hydrogen bonds. We have shown that the symmetric double-well potential in the presence of anharmonic quartic proton–proton interaction gives rise to the anti-kink, anti-soliton, and soliton solutions for the equations of motion. Thereby the proton motion in the form of coherent energy profiles such as kink and solitons may provide the mechanism of bioenergy transport in biological systems.