  Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive
model of long water waves having "good" mathematical and physical properties.
First, the model is a mathematically justified approximation of the exact water
wave problem. Second, the SGN equations are the Euler-Lagrange equations coming
from Hamilton's principle of stationary action with a natural approximate
Lagrangian. Finally, the equations are Galilean invariant which is necessary
for physically relevant mathematical models.
  We have derived the modulation equations to the SGN model and show that they
are strictly hyperbolic for any wave amplitude, i.e., the periodic wave trains
are modulationally stable. Numerical tests for the full SGN equations are
shown. The results confirm the modulational stability analysis.
