Efficient numerical method for solving the direct Zakharov–Shabat scattering problem

Efficient numerical method for solving the direct Zakharov–Shabat scattering problem

A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solution for coupled Gel'fand-Levitan-Marchenko integral equations. Speedup of computations is achieved by using the Toplitz symmetry of the matrix and an "inner bordering" procedure. The new...

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Veröffentlicht in:Journal of the Optical Society of America. B, Optical physics Optical physics, 2015-02, Vol.32 (2), p.290-296
Hauptverfasser: Frumin, Leonid L., Belai, Oleg V., Podivilov, Eugeny V., Shapiro, David A.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Americas
Computation
Integral equations
Joining
Mathematical models
Numerical analysis
Scattering
Symmetry
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Zusammenfassung:A new method to solve the direct Zakharov-Shabat scattering problem is proposed based on the solution for coupled Gel'fand-Levitan-Marchenko integral equations. Speedup of computations is achieved by using the Toplitz symmetry of the matrix and an "inner bordering" procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.
ISSN:0740-3224
1520-8540
DOI:10.1364/JOSAB.32.000290