Numerical study of the soliton waves of the coupled nonlinear Schrِdinger system

A new six-point scheme of the coupled nonlinear Schrِdinger (CNLS) system is derived from the symplectic scheme to study the collision behaviors of soliton waves. We prove that the new six-point scheme preserves the square conservation, which matches the square conservation of the CNLS system. Numerical experiments show that the new six-point scheme has excellent long-time numerical behaviors. From the numerical experiment results we find that the collisions of the soliton waves in the CNLS system are sensitive to the collision velocity and the cross-phase-modulational coefficient.