  Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for
solving ordinary differential equations with additively partitioned right-hand
sides. This work develops symplectic GARK schemes for additively partitioned
Hamiltonian systems. In a general setting, we derive conditions for
symplecticness, as well as symmetry and time-reversibility. We show how
symplectic and symmetric schemes can be constructed based on schemes which are
only symplectic, or only symmetric. Special attention is given to the special
case of partitioned schemes for Hamiltonians split into multiple potential and
kinetic energies. Finally we show how symplectic GARK schemes can leverage
different time scales and evaluation costs for different potentials, and
provide efficient numerical solutions by using different order for these parts.
