2007/08/03 by Francisco Rus, Francisco R. Villatoro · 43 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Amplitude #Ansatz #Computer simulation #Exponent #Function (biology) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical analysis #Optics #Physics #Scaling #Spurious relationship #math-ph #math.MP #msc:35Q51 #msc:35Q53
paper · pdf · doi:10.1016/j.jcp.2007.07.024
published in Journal of Computational Physics 227(1), 440-454 (Elsevier BV) · To be published in Journal of Computational Physics
arxiv created 2007/08/03 · openalex publication_date 2007/08/09 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the Rosenau-Hyman K(p,p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.