  The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that
has been introduced by Clamond et al. to improve the dispersion relation. We
present a precise blow-up scenario of the mSGN equations and we prove the
existence of a class of solutions that develop singularities in finite time.
All the presented results hold also for the Serre-Green-Naghdi system with weak
surface tension.
