  The nonlinear Schroedinger equation is studied for a periodic sequence of
delta-potentials (a delta-comb) or narrow Gaussian potentials. For the
delta-comb the time-independent nonlinear Schroedinger equation can be solved
analytically in terms of Jacobi elliptic functions and thus provides useful
insight into the features of nonlinear stationary states of periodic
potentials. Phenomena well-known from classical chaos are found, such as a
bifurcation of periodic stationary states and a transition to spatial chaos.
The relation of new features of nonlinear Bloch bands, such as looped and
period doubled bands, are analyzed in detail. An analytic expression for the
critical nonlinearity for the emergence of looped bands is derived. The results
for the delta-comb are generalized to a more realistic potential consisting of
a periodic sequence of narrow Gaussian peaks and the dynamical stability of
periodic solutions in a Gaussian comb is discussed.
