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A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation. (English) Zbl 1112.65079
Summary: 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 are conducted and show that this method is quite accurate and describe the interaction picture clearly.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
Full Text: DOI
[1] Ismail, M.S.; Alamri, S.Z., Highly accurate finite difference method for coupled nonlinear Schrödinger equation, Int. J. comp. math., 81, 3, 333-351, (2004) · Zbl 1058.65090
[2] Ismail, M.S.; Taha, Thiab R., Numerical simulation of coupled nonlinear Schrödinger equation, Math. comp. simul., 56, 547-562, (2001) · Zbl 0972.78022
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