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The dynamic equations of the proton transport along the hydrogen bonded molecular systems have been obtained by using completely quantum-mechanical method to be based on new Hamiltonian and model we proposed. Some quantum-mechanical features of the proton-solitons have also been given in such a case. The alternate motion of two defects resulting from proton transfer occurred in the systems can be explained by the results. The results obtained show that the proton-soliton has corpuscle feature and obey classical equations of motion, while the free soliton moves in uniform velocity along the hydrogen bonded chains.

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