Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

Title	Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
Publication Type	Journal Article
Year of Publication	2012
Authors	Grava, T, Klein, C
Journal	Physica D 241, nr. 23-24 (2012): 2246-2264
Keywords	Korteweg-de Vries equation
Abstract	We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.
DOI	10.1016/j.physd.2012.04.001

Research Group:

Mathematics