Soliton tunneling with sub-barrier kinetic energies.

We investigate (theoretically and numerically) the dynamics of a soliton moving in an asymmetrical potential well with a finite barrier. For large values of the width of the well, the width of the barrier, and/or the height of the barrier, the soliton behaves classically. On the other hand, we obtain the conditions for the existence of soliton tunneling with sub-barrier kinetic energies. We apply these results to the study of soliton propagation in disordered systems.