We define a dynamical variable associated with the position of a particle representing the sine-Gordon soliton. Simple relativistic dynamic equations for this particle under the influence of forces are derived, including the case of dissipation. The fluctuation-dissipation theorem for this particle is obtained as well as some results on steady-state velocities and slowing of the thermalization time for ultrarelativistic solitions.
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Bergman et al. (1983) studied this question.
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