A conservative compact finite difference scheme for the KdV equation

Abstract

We propose a new structure-preserving integrator for the Korteweg-de Vries (KdV) equation. In this integrator, two independent structure-preserving techniques are newly combined; the “discrete variational derivative method” for constructing invariants-preserving integrator, and the “compact finite difference method” which is widely used in the area of numerical fluid dynamics for resolving wave propagation phenomena. Numerical experiments show that the new integrator is in fact advantageous than the existing integrators.