  For surface gravity waves propagating in shallow water, we propose a variant
of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter
that can be chosen to improve the dispersion properties. The novelty here
consists in the fact that the new model conserves the energy, contrary to other
modified Serre's equations found in the literature. Numerical comparisons with
the Euler equations show that the new model is substantially more accurate than
the classical Serre equations, specially for long time simulations and for
large amplitudes.
