Range Proton Transport at Interfaces Soliton Theory

Long-Range Proton Transport at Interfaces Soliton Theory 

To describe traveling wave solutions, it is customary to introduce a wave coordinate f = X - uf, with soliton velocity v. Integrating the equation of motion once gives 

Solution of Equation 2.60 gives expressions for the soliton energy. 

A standard approach was adopted to find the soliton mobility in the equation of motion, additional terms representing a viscous friction and an external force/, acting on each hydronium ion, were added. The terminal drift velocity was calculated. The ratio of drift velocity to external force, evaluated in the limit/ 0, gives the mobility of the soliton, 

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