  We report on phenomenon of Anderson-type localization of walking solitons in
optical lattices with random frequency modulation, manifested as dramatic
enhancement of soliton trapping probability on lattice inhomogeneities with
growth of the frequency fluctuation level. The localization process is strongly
sensitive to the lattice depth since in shallow lattices walking solitons
experience random refraction and/or multiple scattering in contrast to
relatively deep lattices, where solitons are typically immobilized in the
vicinity of local minimums on modulation frequency.
