  We extend our studies of thermal diffusion of non-topological solitons to
anharmonic FPU-type chains with additional long-range couplings. The observed
superdiffusive behavior in the case of nearest neighbor interaction (NNI) turns
out to be the dominating mechanism for the soliton diffusion on chains with
long-range interactions (LRI). Using a collective variable technique in the
framework of a variational analysis for the continuum approximation of the
chain, we derive a set of stochastic integro-differential equations for the
collective variables (CV) soliton position and the inverse soliton width. This
set can be reduced to a statistically equivalent set of Langevin-type equations
for the CV, which shares the same Fokker-Planck equation. The solution of the
Langevin set and the Langevin dynamics simulations of the discrete system agree
well and demonstrate that the variance of the soliton increases stronger than
linearly with time (superdiffusion). This result for the soliton diffusion on
anharmonic chains with long-range interactions reinforces the conjecture that
superdiffusion is a generic feature of non-topological solitons.
