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We consider wavepackets composed of two modulated carrier Bloch waves withopposite group velocities in the one dimensional periodic NonlinearSchroedinger/Gross-Pitaevskii equation. These can be approximated by firstorder coupled mode equations (CMEs) for the two slowly varying envelopes. Undera suitably selected periodic perturbation of the periodic structure the CMEspossess a spectral gap of the corresponding spatial operator and allow familiesof exponentially localized solitary waves parametrized by velocity. This leadsto a family of approximate solitary waves in the periodic nonlinearSchroedinger equation. Besides a formal derivation of the CMEs a rigorousjustification of the approximation and an error estimate in the supremum normare provided. Several numerical tests corroborate the analysis.

Justification of the Coupled Mode Asymptotics for Localized Wavepackets in the Periodic Nonlinear Schr\"odinger Equation