It is shown that the acceleration of the sine-Gordon solitons by a constant torque increases as t² for small times t. For larger times, the velocity behaves like tanh t³. Thus the soliton dynamical behavior is not Newtonian. Analytical arguments are given based on the linear perturbation theory which generalize this conclusion to any weak external perturbation of sine-Gordon solitons.
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Fernandez et al. (1981) studied this question.
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