Numerical study of the 2D Kaup-Broer-Kuperschmidt Boussinesq system
This work addresses the stability of soliton solutions in a specific 2D Boussinesq system, but the results are incremental as they confirm expected instability without providing new constructive insights.
The study numerically investigates the 2D Kaup-Broer-Kuperschmidt Boussinesq system, finding that soliton-type solutions are unstable against dispersion and singularity formation, and no stable structures were observed.
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.