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We investigate the existence and stability of quiescent gap solitons in a system of two linearly coupled Bragg gratings with cubic-quintic nonlinearity. It is found that the model supports two disjoint families of solitons that fill the entire bandgap. There exist symmetric and asymmetric solitons in each family. Exact analytical solutions of symmetric solitons for both families are found. The stability of solitons is investigated by means of systematic numerical stability analysis. The effect of quintic nonlinearity and coupling coefficient on the stability of solitons and the stability regions are analyzed.

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