(2   1)-dimensional compacton solutions with and without completely elastic interaction properties

Taking the (2 + 1)-dimensional Broer–Kaup–Kupershmidt system as a simple example, some special types of (2 + 1)-dimensional compacton solutions are constructed. It is shown that there is quite rich interaction behaviour between two travelling compactons. For some types of compactons, the interactions among them may not be completely elastic. For some others, the interactions are completely elastic. There is no phase shift for the interactions of the (2 + 1)-dimensional compactons discussed in this paper.