Drift instability and tunneling of lattice solitons

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.