Sine-Gordon Solitons Do Not Behave Like Newtonian Particles

Abstract

It is shown that the acceleration of the sine-Gordon solitons by a constant torque increases as $t^2$ for small times $t$. For larger times, the velocity behaves like tanh $t^3$. 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.