A New Six Point Finite Difference Scheme for Nonlinear Waves Interaction Model

Abstract

In the paper, the coupled 1D Klein-Gordon-Zakharov system (KGZ-equations in short) is considered as the model equation for wave-wave interaction in ionic media. A finite difference scheme is derived for the model equations. A new six point scheme, which is equivalent to the multi-symplectic integrator, is derived. The numerical simulation is also presented for the model equations.

Keywords: Coupled 1D Klein-Gordon-Zakharov system; Energy conservation; Six-point scheme