Additivity of diffusion coefficients for solitons

The problem of soliton diffusion was studied by employing a Boltzmann type of kinetic equation. Two classes of scattering processes were considered: I) those preserving the integrability of the system and leading to coordinate shifts without momentum change and II) those destroying the integrability and leading to momentum transfer without coordinate shift. If was found that the total diffusion coefficient D is the sum of DI and DII. A physical explanation for this counterintuitive result is presented. As an example, the sine-Gordon system with impurities is considered.