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arXiv · 1105.1717

On the properties of compacton-anticompacton collisions

Andres Cardenas·Bogdan Mihaila·Fred Cooper·Avadh Saxena
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Abstract

We study the properties of compacton-anticompacton collision processes. We compare and con- trast 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 Padé 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 "annihila- tion" 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 waveform.

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Andres Cardenas, Bogdan Mihaila, Fred Cooper, Avadh Saxena. 2011-05-09. On the properties of compacton-anticompacton collisions. https://doi.org/10.1103/physreve.83.066705

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