  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 generalizes these GARK schemes to symplectic GARK schemes for
additively partitioned Hamiltonian systems. In a general setting, we derive
conditions for symplecticeness, as well as symmetry and time-reversibility. We
show how symplectic and symmetric schemes can be constructed based on schemes
which are only symplectic. 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 use efficiently
different time scales and evaluation costs for different potentials by using
different order for these parts.
