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Higher-Order Split-Step Schemes for the Generalized Nonlinear Schrödinger Equation

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Gulcin M. Muslu

    (Istanbul Technical University, Department of Mathematics)

  • Husnu A. Erbay

    (Istanbul Technical University, Department of Mathematics)

Abstract

Summary The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational cost. This numerical experiment shows that the split-step Fourier method provides highly accurate solutions for the GNLS equation. Furthermore, two test problems concerning the interaction of two solitary waves and an exact solution which blows up in finite time are investigated by using the fourth-order split-step scheme and particular attention is paid to the conserved quantities as an indicator of the accuracy.

Suggested Citation

  • Gulcin M. Muslu & Husnu A. Erbay, 2004. "Higher-Order Split-Step Schemes for the Generalized Nonlinear Schrödinger Equation," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 658-667, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_64
    DOI: 10.1007/978-3-642-18775-9_64
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