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A differential quadrature algorithm for nonlinear Schrödinger equation

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Abstract

Numerical solutions of a nonlinear Schrödinger equation is obtained using the differential quadrature method based on polynomials for space discretization and Runge–Kutta of order four for time discretization. Five well-known test problems are studied to test the efficiency of the method. For the first two test problems, namely motion of single soliton and interaction of two solitons, numerical results are compared with earlier works. It is shown that results of other test problems agrees the theoretical results. The lowest two conserved quantities and their relative changes are computed for all test examples. In all cases, the differential quadrature Runge–Kutta combination generates numerical results with high accuracy.

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Authors and Affiliations

  1. Anadolu Guzel Sanatlar Lisesi, Kütahya, Turkey

    Alper Korkmaz

  2. Osmangazi University, Eskişehir, Turkey

    İdris Dağ

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  1. Alper Korkmaz
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  2. İdris Dağ
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Correspondence to Alper Korkmaz.

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Korkmaz, A., Dağ, İ. A differential quadrature algorithm for nonlinear Schrödinger equation. Nonlinear Dyn 56, 69–83 (2009). https://doi.org/10.1007/s11071-008-9380-0

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  • DOI: https://doi.org/10.1007/s11071-008-9380-0

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