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Numerical simulation of coupled nonlinear Schrödinger equation

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  • Ismail, M.S.
  • Taha, Thiab R.

Abstract

The coupled nonlinear Schrödinger equation models several interesting physical phenomena. It represents a model equation for optical fiber with linear birefringence. In this paper we introduce a finite difference method for a numerical simulation of this equation. This method is second-order in space and conserves the energy exactly. It is quite accurate and describes the interaction picture clearly according to our numerical results.

Suggested Citation

  • Ismail, M.S. & Taha, Thiab R., 2001. "Numerical simulation of coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(6), pages 547-562.
    • Handle: RePEc:eee:matcom:v:56:y:2001:i:6:p:547-562
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    Citations

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    Cited by:

    1. Ismail, M.S., 2008. "Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 532-547.
    2. Zhou, Shenggao & Cheng, Xiaoliang, 2010. "Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2362-2373.
    3. Todorov, M.D. & Christov, C.I., 2009. "Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector NLSE," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 46-55.
    4. Sonnier, W.J. & Christov, C.I., 2005. "Strong coupling of Schrödinger equations: Conservative scheme approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 514-525.
    5. Ilati, Mohammad & Dehghan, Mehdi, 2019. "DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose–Einstein condensates," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 244-253.
    6. Tsang, S.C. & Chow, K.W., 2004. "The evolution of periodic waves of the coupled nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 551-564.
    7. Wang, Tingchun & Nie, Tao & Zhang, Luming & Chen, Fangqi, 2008. "Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 607-621.
    8. Lin, Bin, 2019. "Parametric spline schemes for the coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 58-69.
    9. Ismail, M.S. & Taha, Thiab R., 2007. "A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 302-311.
    10. Taghread Ghannam Alharbi & Abdulghani Alharbi, 2023. "A Study of Traveling Wave Structures and Numerical Investigations into the Coupled Nonlinear Schrödinger Equation Using Advanced Mathematical Techniques," Mathematics, MDPI, vol. 11(22), pages 1-16, November.

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