A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation

The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in space and time and conserves the energy exactly. Many numerical experiments have been conducted and have shown that this method is quite accurate and describe the interaction picture clearly.