Classical Particlelike Behavior of Sine-Gordon Solitons in Scattering Potentials and Applied Fields

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Abstract
We show that classical sine-Gordon solitons maintain their integrity to a high degree in the presence of external perturbations. Two examples, of particular importance in condensed matter, are described in detail: (i) A model impurity is found to bind low-velocity solitons but merely phase shift those with high velocities, and (ii) external static driving terms with damping accelerate the soliton to a terminal velocity. The importance of a translation mode is emphasized and it is concluded that the soliton behaves as a classical particle in all essential respects.