Thermal corrections to overdamped soliton motion

A singular perturbation theory is developed for evaluating the thermal effects on over-damped soliton motion. I find that the mobility of an overdamped sine-Gordon kink in the static limit is the same as given by Büttiker and Landauer and that the effect of an increase in the temperature is to increase this mobility by the factor [$1+\frac{\left(1.075\mathrm{}\dots \right)}{\beta }{E}_0+\cdots$], where $E_0$ is the rest energy of a kink. I also evaluate the change in the shape of an over-damped sine-Gordon kink caused by thermal fluctuations and find that the kink somewhat flattens, increasing its width.