2007/01/01 by Bogdan Mihaila, Andres Cardenas, Fred Cooper +4
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Botnet #Computer network #Computer science #Computer security #Denial-of-service attack #Internet Traffic Analysis and Secure E-voting #Mathematical economics #Mathematics #Network Security and Intrusion Detection #Network Traffic and Congestion Control #Network packet #Nonlinear Waves and Solitons #Overhead (engineering) #Password #Physics #Router #Routing protocol #Stability (learning theory) #Stability and Controllability of Differential Equations #Statistical physics #The Internet #nlin.PS
paper · pdf · doi:10.1103/physreve.82.066702
published as Phys. Rev. E 82, 066702 (2010) · 8 figures
openalex publication_date 2007/01/01 · arxiv created 2010/11/05 · arxiv updated 2015/05/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/26
Extending a Padé 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.