  In this short communication we present the multi-symplectic structure for the
two-layer Serre-Green-Naghdi equations describing the evolution of large
amplitude internal gravity long waves. We consider only a two-layer
stratification with rigid bottom and lid for simplicity, generalisations to
several layers being straightforward. This multi-symplectic formulation allows
the application of various multi-symplectic integrators (such as Euler or
Preissman box schemes) that preserve exactly the multi-symplecticity at the
discrete level.
