Multisymplectic Euler Box Scheme for the KdV Equation

We investigate the multisymplectic Euler box scheme for the Korteweg--de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky- Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.