Numerical study of the 2D Kaup-Broer-Kuperschmidt Boussinesq system
Th\'eo Gaudry, Christian Klein, Jean-Claude Saut, Nikola Stoilov
TL;DR
This paper numerically investigates the 2D Kaup-Broer-Kuperschmidt Boussinesq system, revealing the instability of soliton solutions and the absence of stable localized structures.
Contribution
It provides the first numerical analysis of soliton stability in the 2D Kaup-Broer-Kuperschmidt Boussinesq system, highlighting their inherent instability.
Findings
Soliton solutions are unstable against dispersion and singularity formation.
Line solitons and localized initial data do not produce stable structures.
Numerical methods confirm the instability of solitons in this system.
Abstract
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.
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