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Finite difference methods for an AKNS eigenproblem

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  • Weideman, J.A.C.
  • Herbst, B.M.

Abstract

We consider the numerical solution of the AKNS eigenproblem associated with the nonlinear Schrödinger equation. Four finite difference methods are considered: two standard schemes (forward and central differences), a discretization introduced by Ablowitz and Ladik (1976), and a modified version of the latter scheme. By comparing these methods both numerically and theoretically we show that the modified Ablowitz-Ladik scheme has several desirable features. This includes the property that with a given number of gridpoints it approximates much larger sections of the spectrum than its rivals.

Suggested Citation

  • Weideman, J.A.C. & Herbst, B.M., 1997. "Finite difference methods for an AKNS eigenproblem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 77-88.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:1:p:77-88
    DOI: 10.1016/S0378-4754(96)00057-2
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    Cited by:

    1. Julian Hoxha & Wael Hosny Fouad Aly & Erdjana Dida & Iva Kertusha & Mouhammad AlAkkoumi, 2022. "A Novel Optical-Based Methodology for Improving Nonlinear Fourier Transform," Mathematics, MDPI, vol. 10(23), pages 1-20, November.

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