A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

In this paper, time‐splitting spectral approximation technique has been proposed for Chen‐Lee‐Liu (CLL) equation involving Riesz fractional derivative. The proposed numerical technique is efficient, unconditionally stable, and of second‐order accuracy in time and of spectral accuracy in space. Moreo...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2019-01, Vol.42 (1), p.99-114
Main Author: Saha Ray, Santanu
Format: Article
Language:English
Subjects:
Chen‐Lee‐Liu equation
CN‐WSGD method
Grünwald‐Letnikov difference operator
Optical fibers
Riesz fractional derivative
Spectra
Spectral methods
Splitting
time‐splitting spectral method
weighted shifted Grünwald‐Letnikov formula
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Summary:In this paper, time‐splitting spectral approximation technique has been proposed for Chen‐Lee‐Liu (CLL) equation involving Riesz fractional derivative. The proposed numerical technique is efficient, unconditionally stable, and of second‐order accuracy in time and of spectral accuracy in space. Moreover, it conserves the total density in the discretized level. In order to examine the results, with the aid of weighted shifted Grünwald‐Letnikov formula for approximating Riesz fractional derivative, Crank‐Nicolson weighted and shifted Grünwald difference (CN‐WSGD) method has been applied for Riesz fractional CLL equation. The comparison of results reveals that the proposed time‐splitting spectral method is very effective and simple for obtaining single soliton numerical solution of Riesz fractional CLL equation.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5326