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Strong coupling of Schrödinger equations: Conservative scheme approach

Author

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  • Sonnier, W.J.
  • Christov, C.I.

Abstract

The system of coupled nonlinear Schrödinger’s equations (CNLSE) is considered and the physical meaning of the coupling terms is identified. The attention is focused on the case of real-valued parameter of linear cross-diffusion. A new analytical solution for the coupled case is found and used as initial condition for the interaction and evolution of two pulses.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:69:y:2005:i:5:p:514-525
    DOI: 10.1016/j.matcom.2005.03.016
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    References listed on IDEAS

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    1. 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.
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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. 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.
    3. Todorov, M.D., 2016. "The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled systems of Nonlinear Schrödinger Equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 273-286.
    4. Todorov, M.D. & Christov, C.I., 2012. "Collision dynamics of elliptically polarized solitons in Coupled Nonlinear Schrödinger Equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1321-1332.
    5. 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.
    6. 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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