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We derive an analytic formula for the lateral dynamics of solitons in ageneral inhomogeneous nonlinear media, and show that it can be valid over tensof diffraction lengths. In particular, we show that solitons centered at alattice 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.

Drift instability and tunneling of lattice solitons