Efficient schemes for the coupled Schrödinger-KdV equations: Decoupled and conserving three invariants

We give a systematic method for discretizing Hamiltonian partial differential equations. An application of the method to the Hamiltonian form of the coupled Schrödinger-KdV equations yields a temporal first-order conservative scheme. Temporal second- and fourth-order schemes are developed by employing the composition method. All the schemes are decoupled and exactly conserve three invariants simultaneously. Numerical results show good performance of the schemes and verify the theoretical results.