Interactions between quiescent gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity are systematically investigated. In a previous work, it was found that the model supports symmetric and asymmetric soliton solutions. For each of these categories, there exist two disjoint families of quiescent gap solitons. One family can be regarded as the generalization of the quiescent gap solitons in dual-core Bragg gratings with Kerr nonlinearity (called Type 1). On the other hand, the other family is found in the region, where the quintic nonlinearity is dominant (called Type 2). The interactions of in-phase Type 1 asymmetric solitons result in a range of outcomes, namely, fusion into a single zero-velocity soliton, asymmetrical separation of solitons, symmetrical separation of solitons, formation of three solitons, and the destruction of solitons. In the case of symmetric solitons, interactions of in-phase Type 1 solitons may lead to fusion in the form of a quiescent soliton, asymmetrically separating solitons, or the formation of three solitons. It is also found that the interaction of in-phase asymmetric Type 2 solitons results in their destruction. Also, the effects of the quintic nonlinearity, coupling coefficients, initial separation, and initial phase difference on the outcomes of the interactions are analyzed. Also, in the case of asymmetric solitons, the outcomes of the soliton-soliton interactions for specular-symmetric and crosssymmetric initial configurations are compared.
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