Numerical Study of the Peregrine–Boussinesq System in 2D

ABSTRACT

A numerical study of the 2D Peregrine–Boussinesq or Amick–Schonbek system is presented. Numerical evidence is given for the transverse stability of the 1D solitary waves that are line solitary waves of the 2D equations. It is shown that initial data not satisfying the noncavitation condition can lead to the formation of a gradient catastrophe in finite time. The numerical propagation of localized smooth initial data does not lead to the formation of stable structures localized in both spatial directions. For initial data satisfying the noncavitation condition, smooth solutions appear to exist for all times.