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

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

2012-02-05

arxiv.org/abs/1202.0962v2

Physics

Mathematical Physics

Scientific paper

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.

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