  We derive an analytic formula for the lateral dynamics of solitons in a
general inhomogeneous nonlinear media, and show that it can be valid over tens
of diffraction lengths. In particular, we show that solitons centered at a
lattice maximum can be ``mathematically unstable'' but ``physically stable''.
We also derive an analytic upper bound for the critical velocity for tunneling,
which is valid even when the standard Peierls-Nabarro potential approach fails.
