Numerical study of the 2D Kaup-Broer-Kuperschmidt Boussinesq system

In this work we consider the well posed version of the Kaup-Broer-Kuperschmidt system in two dimensions. We numerically construct soliton type solutions and show that they are unstable both against dispersion and singularity formation. Further, we study line solitons and their stability, as well as generally localised initial data. In either case we fail to find stable structures.