  A new approximation for evolution described by Nonlinear Schrodinger Equation
(NLS) with periodic potential is presented. It relies on restricting dynamics
to one band of the bandgap spectrum, and taking into account only one,
dominating Fourier component in the nonlinear Bloch-wave mixing. The resulting
equation has a simple, discrete form in the basis of linear Wannier functions,
and turns out to be very accurate as long as the modes in other bands are not
excited and the potential is not very deep. Widely used approximations, the
tight-binding approximation and the effective mass approximation, are derived
from the new equation as the limiting cases.
