Stability and dynamical properties of Cooper-Shepard-Sodano compactons

Journal Article · Wed Dec 15 04:00:00 EST 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.066702· OSTI ID:21502902

Mihaila, Bogdan ^[1]; Cardenas, Andres ^[1]; Cooper, Fred ^[2]; Saxena, Avadh ^[3]

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1. Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Santa Fe Institute, Santa Fe, New Mexico 87501 (United States)
3. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons re-emerge with same coherent shape when scattered. The time evolution of the small-amplitude ripple resulting after scattering depends on the values of the parameters l and p characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability than in the case of RH compacton propagation.

• OSTI ID: 21502902
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 6 Vol. 82; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
EQUATIONS
EVOLUTION
HAMILTONIANS
MATHEMATICAL EVOLUTION
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
QUANTUM OPERATORS
SCATTERING
SIMULATION
STABILITY