  We study nonlinear states for NLS-type equation with additional periodic
potential U(x) (called the Gross-Pitaevskii equation, GPE, in theory of
Bose-Einstein Condensate, (BEC)). We prove that if the nonlinearity is
defocusing (repulsive, in BEC context) then under certain conditions there
exists a homeomorphism between the set of nonlinear states for GPE (i.e. real
bounded solutions of some nonlinear ODE) and the set of bi-infinite sequences
of numbers from 1 to N for some integer N. These sequences can be viewed as
codes of the nonlinear states. Sufficient conditions for the homeomorphism to
exist are given in the form of three hypotheses. For a given U(x), the
verification of the hypotheses should be done numerically. We report on
numerical results for the case of GPE with cosine potential and describe
regions in the plane of parameters where this coding is possible.
