Properties of compacton-anticompacton collisions

We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l=p=2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p=1 and l=3. This study is performed using a Pad\'e discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton-anticompacton scattering. For the CSS equation, the scattering can be interpreted as ``annihilation'' as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision, which eventually lead to ``blowup'' of the resulting wave form.