A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations

In this paper, a conservative compact finite difference scheme is presented to numerically solve the coupled Schrödinger-KdV equations. The analytic solutions of the coupled equations have some invariants such as the number of plasmons, the number of particles, and the energy of oscillations, and we proved that the compact difference scheme preserves those invariants in discrete sense. Optimal order convergence rate of the proposed linearized compact scheme was analyzed. Numerical experiments on model problems show that the scheme is of high accuracy.