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 << 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.

A numerical study of the small dispersion limit of the Korteweg–de Vries equation and asymptotic solutions / Grava, Tamara; Klein, C.. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 241:23-24(2012), pp. 2246-2264. [10.1016/j.physd.2012.04.001]

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

Grava, Tamara;
2012-01-01

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 << 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.
2012
241
23-24
2246
2264
https://arxiv.org/abs/1202.0962
Grava, Tamara; Klein, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14938
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