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Some efficient temporal first-, second- and higher-order numerical schemes are constructed for the coupled nonlinear Schr?dinger-Boussinesq （CNSB） equations based on discretizing the Hamiltonian formula by an exponential method in a compact representation, discrete gradient method and composition method. The schemes are fully decoupling of the three solution components, which is distinct from the partially decoupled scheme in the literature, and their compact representation reduces the storage requirement and operation count. Rigorous analyses are carried out to show the exact preservation of the discrete energy for the proposed schemes. Numerical experiments verify the theoretical results and confirm the satisfactory solution accuracy and excellent efficiency of the present schemes.
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