Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method

In this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schrödinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some ill...

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Main Authors:	Nehad Ali Shah, Praveen Agarwal, Jae Dong Chung, Essam R. El-Zahar, Y. S. Hamed
Format:	Article
Language:	English
Published:	MDPI AG 2020-11-01
Series:	Symmetry
Subjects:	Fiber optics nonlinear Schrödinger equations fractional calculus iterative transform method analytic solution
Online Access:	https://www.mdpi.com/2073-8994/12/11/1850

id	doaj-640fa8e9f35642919723e0bb691d7826
record_format	Article
spelling	doaj-640fa8e9f35642919723e0bb691d78262020-11-25T04:07:02ZengMDPI AGSymmetry2073-89942020-11-01121850185010.3390/sym12111850Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform MethodNehad Ali Shah0Praveen Agarwal1Jae Dong Chung2Essam R. El-Zahar3Y. S. Hamed4Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 58307, VietnamDepartment of Mathematics, Anand International College of Engineering, Jaipur 302003, IndiaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, KoreaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaIn this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schrödinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some illustrative examples are presented to show the validity of the proposed technique without using any polynomials. The proposed method provides the series form solutions, which converge to the exact results. Using the present methodology, the solutions of fractional-order problems as well as integral-order problems are calculated. The present method has less computational costs and a higher rate of convergence. Therefore, the suggested algorithm is constructive to solve other fractional-order linear and nonlinear partial differential equations.https://www.mdpi.com/2073-8994/12/11/1850Fiber opticsnonlinear Schrödinger equationsfractional calculusiterative transform methodanalytic solution
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nehad Ali Shah Praveen Agarwal Jae Dong Chung Essam R. El-Zahar Y. S. Hamed
spellingShingle	Nehad Ali Shah Praveen Agarwal Jae Dong Chung Essam R. El-Zahar Y. S. Hamed Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method Symmetry Fiber optics nonlinear Schrödinger equations fractional calculus iterative transform method analytic solution
author_facet	Nehad Ali Shah Praveen Agarwal Jae Dong Chung Essam R. El-Zahar Y. S. Hamed
author_sort	Nehad Ali Shah
title	Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method
title_short	Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method
title_full	Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method
title_fullStr	Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method
title_full_unstemmed	Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method
title_sort	analysis of optical solitons for nonlinear schrödinger equation with detuning term by iterative transform method
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2020-11-01
description	In this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schrödinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some illustrative examples are presented to show the validity of the proposed technique without using any polynomials. The proposed method provides the series form solutions, which converge to the exact results. Using the present methodology, the solutions of fractional-order problems as well as integral-order problems are calculated. The present method has less computational costs and a higher rate of convergence. Therefore, the suggested algorithm is constructive to solve other fractional-order linear and nonlinear partial differential equations.
topic	Fiber optics nonlinear Schrödinger equations fractional calculus iterative transform method analytic solution
url	https://www.mdpi.com/2073-8994/12/11/1850
work_keys_str_mv	AT nehadalishah analysisofopticalsolitonsfornonlinearschrodingerequationwithdetuningtermbyiterativetransformmethod AT praveenagarwal analysisofopticalsolitonsfornonlinearschrodingerequationwithdetuningtermbyiterativetransformmethod AT jaedongchung analysisofopticalsolitonsfornonlinearschrodingerequationwithdetuningtermbyiterativetransformmethod AT essamrelzahar analysisofopticalsolitonsfornonlinearschrodingerequationwithdetuningtermbyiterativetransformmethod AT yshamed analysisofopticalsolitonsfornonlinearschrodingerequationwithdetuningtermbyiterativetransformmethod
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Analysis of Optical Solitons for Nonlinear Schrödinger Equation with Detuning Term by Iterative Transform Method

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