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We study the properties of the proton transfer in hydrogen-bonded molecule systems exposed in an externally applied fields in our model and give also the equations of motion of the protons and its corresponding soliton-solutions in such a case. Based on these results we calculate further the mobility and electric-conductivity of the proton transfer driven by an externally applied electric-field in the systems, which are about (9.2-9.7) x 10(-6) m(2)/V s and (1.47-1.55) x 10(-2) (Omegam)(-1) for the ice, respectively. This value for the mobility coincides quite with experimental result of (1-10) x 10(-2) cm(2)/V S. (C) 2004 Elsevier B.V. All rights reserved.

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