  A detailed numerical study of solutions to the Serre-Green-Naghdi (SGN)
equations in 2D with vanishing curl of the velocity field is presented. The
transverse stability of line solitary waves, 1D solitary waves being exact
solutions of the 2D equations independent of the second variable, is
established numerically. The study of localized initial data as well as
crossing 1D solitary waves does not give an indication of existence of stable
structures in SGN solutions localized in two spatial dimensions. For the
numerical experiments, an approach based on a Fourier spectral method with a
Krylov subspace technique is applied.
