© 2019 Wiley Periodicals, Inc. The general Degasperis–Procesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We propose a finite-difference scheme for this equation that preserves some conservation and balance laws. In addition, the stability of the scheme and the convergence of numerical solutions to exact solutions for solitons are proved. Numerical experiments confirm the theoretical conclusions. For essentially nonintegrable versions of the gDP equation, it is shown that solitons and antisolitons collide almost elastically: they retain their shape after interaction, but a small “tail”, the so-called “radiation”, appears.
|Idioma original||Inglés estadounidense|
|Número de páginas||19|
|Publicación||Numerical Methods for Partial Differential Equations|
|Estado||Publicada - 1 jul 2020|