A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers. (8th November 2018)

• Record Type: Journal Article
• Authors: Saha Ray, Santanu
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 1(2019)
• Page Start: 99
• Page End: 114
• Publication Date: 2018-11-08
• Subjects: Chen‐Lee‐Liu equation -- CN‐WSGD method -- Grünwald‐Letnikov difference operator -- Riesz fractional derivative -- time‐splitting spectral method -- weighted shifted Grünwald‐Letnikov formula; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5326
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.