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We propose and study two finite difference schemes (FDSs) for the double dispersion equations. The first FDS is symplectic, while the second one preserves the discrete momentum exactly. Both FDS conserve the discrete energy approximately with O(h2+τ2)$O(h^{2}+\tau ^{2})$ global error. The extensive numerical experiments agree well with the theoretical results for single solitary wave as well as for the interaction between two solitary waves.

Invariant preserving schemes for double dispersion equations