A finite difference scheme for the K(2, 2) compacton equation
Journal of Computational Physics
A numerical study of compactons
Mathematics and Computers in Simulation
Patterns on liquid surfaces: cnoidal waves, compactons and scaling
Physica D - Special issue on nonlinear waves and solitons in physical systems
On a class of nonlinear dispersive-dissipative interactions
Physica D - Special issue on nonlinear waves and solitons in physical systems
Particle methods for dispersive equations
Journal of Computational Physics
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
Method of lines study of nonlinear dispersive waves
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Padé numerical method for the Rosenau-Hyman compacton equation
Mathematics and Computers in Simulation
Adiabatic perturbations for compactons under dissipation and numerically-induced dissipation
Journal of Computational Physics
Hi-index | 31.45 |
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.