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Variational iteration method for coupled nonlinear Schrödinger equations. (English) Zbl 1141.65387
Summary: 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.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations