  An energy conservative discontinuous Galerkin scheme for a generalised third
order KdV type equation is designed. Based on the conservation principle, we
propose techniques that allow for the derivation of optimal a priori bounds for
the linear KdV equation and a posteriori bounds for the linear and modified KdV
equation. Extensive numerical experiments showcasing the good long time
behaviour of the scheme are summarised which are in agreement with the analysis
proposed.
