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

被引：25
|
作者：
Grava, T. [2 ]
Klein, C. [1 ]
机构：
[1] Univ Bourgogne, Inst Math Bourgogne, F-21078 Dijon, France
[2] SISSA, I-34136 Trieste, Italy
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2012年 / 241卷 / 23-24期
基金：
欧洲研究理事会;
关键词：
Korteweg-de Vries equation; Dispersive shocks; Multi-scale analysis; Numerical methods; DOUBLE SCALING LIMIT; ORTHOGONAL POLYNOMIALS; MULTISCALE EXPANSION; DEVRIES EQUATION; CAMASSA-HOLM; UNIVERSALITY; EIGENVALUES; RESPECT; SYSTEMS; ZONE;
D O I：
10.1016/j.physd.2012.04.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2012 Elsevier B.V. All rights reserved.
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页码：2246 / 2264
页数：19
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