On the properties of compacton-anticompacton collisions
arXiv:1105.1717 · doi:10.1103/PhysRevE.83.066705
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.
8 pages, 7 figures
References in corpus (5)
- Compact self-gravitating solutions of quartic (K) fields in brane cosmology
- Degenerate dispersive equations arising in the study of magma dynamics
- Stability and dynamical properties of Rosenau-Hyman compactons using Pade approximants
- Stability and dynamical properties of Cooper-Shepard-Sodano compactons
- On a Hamiltonian PDE arising in Magma Dynamics