We study nonlinear states for the NLS-type equation with additional periodic potential U(x), also called the Gross–Pitaevskii equation, GPE, in theory of Bose–Einstein Condensate, BEC. We prove that if the nonlinearity is defocusing (repulsive, in the BEC context) then under some conditions there exists a homeomorphism between the set of all nonlinear states for GPE (i.e. real bounded solutions of...
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