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Local structure-preserving algorithms including multi-symplectic,local energy-and momentum-preserving schemes are proposed for the generalized Rosenau-RLW-KdV equation based on the multi-symplectic Hamiltonian formula of the equation.Each of the present algorithms holds a discrete conservation law in any time-space region.For the original problem subjected to appropriate boundary conditions,these algorithms will be globally conservative.Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes.Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invadants.