Numerical integration of coupled Korteweg-de Vries System
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Mathematical Physics
math.MP
Abstract
We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes. The method is applied to Hirota-Satsuma (HS) system and compared with its known explicit solution investigating the influence of initial conditions and grid sizes on accuracy. We also illustrate the method to show the effects of constants with a transition to non-integrable cases.
Keywords
Cite
@article{arxiv.math/0211453,
title = {Numerical integration of coupled Korteweg-de Vries System},
author = {A. A. Halim and S. P. Kshevetskii and S. B. Leble},
journal= {arXiv preprint arXiv:math/0211453},
year = {2025}
}
Comments
11 pages, 13 figures