𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Numerical integration of a coupled Korteweg-de Vries system

✍ Scribed by A.A. Halim; S.P. Kshevetskii; S.B. Leble

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
787 KB
Volume
45
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

introduce a numerical method for general coupled Korteweg-deVries systems. The scheme is valid for solving Cauchy problems for an 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 the 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 nonintegrable cases.

πŸ“œ SIMILAR VOLUMES

Numerical solution of a coupled Korteweg
Numerical solution of a coupled Korteweg–de Vries equations by collocation method
✍ M.S. Ismail πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 223 KB

## Abstract A numerical method for solving the coupled Korteweg‐de Vries (CKdV) equation based on the collocation method with quintic B‐spline finite elements is set up to simulate the solution of CKdV equation. Invariants and error norms are studied wherever possible to determine the conservation

The coupling integrable couplings of the
The coupling integrable couplings of the modified Korteweg–de Vries (mKdV) hierarchy
✍ Xiurong Guo πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 223 KB

a b s t r a c t Two kinds of coupling integrable couplings of the mKdV hierarchy are obtained, respectively, by making use of two higher-dimensional Lie algebras in the vector forms. The Hamiltonian structure of one reduced coupling integrable coupling of them is worked out by employing the variatio