A Note on the Construction of Symplectic Schemes for Splitable Hamiltonian H = H(1) + H(2) + H(3)

Abstract

In this note, we will give a proof for the uniqueness of 4th-order time-reversible symplectic difference schemes of 13th-fold compositions of phase flows $\phi ^t_{H(1)}, \phi ^t_{H(2)}, \phi ^t_{H(3)}$ with different temporal parameters for splitable hamiltonian $H=H^{(1)}+H^{(2)}+H^{(3)}$.