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

作者：Grava T; Klein C^*

来源：Physica D: Nonlinear Phenomena , 2012, 241(23-24): 2246-2264.

DOI：10.1016/j.physd.2012.04.001

• Korteweg-de Vries equation
• Dispersive shocks
• Multi-scale analysis
• Numerical methods

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 %26lt;%26lt; 1 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.

• 出版日期2012-12-1