Variational iteration method for coupled nonlinear Schrödinger equations

In this paper, we apply the variational iteration method proposed by Ji-Huan He to simulate numerically a system of two coupled nonlinear one-dimensional Schrödinger equations subjected initially to a prescribed periodic wave solution. Test examples are given to demonstrate the accuracy and capability of the method with different wave–wave interaction coefficients. The accuracy of the method is verified by ensuring that the energy conservation remains almost constant. The numerical results obtained with a minimum amount of computation show that the variational iteration method is much easier, more convenient and efficient for solving nonlinear partial differential equations.