Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional

In this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D,...

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Main Authors:	Wei Gao, Hajar F. Ismael, Sizar A. Mohammed, Haci Mehmet Baskonus, Hasan Bulut
Format:	Article
Language:	English
Published:	Frontiers Media S.A. 2019-11-01
Series:	Frontiers in Physics
Subjects:	paraxial wave equation complex soliton extended sinh-Gordon method soliton structures contour surfaces
Online Access:	https://www.frontiersin.org/article/10.3389/fphy.2019.00197/full

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spelling	doaj-ac3a7c1ce86f43f4a0d1f2916e2c88702020-11-25T02:16:46ZengFrontiers Media S.A.Frontiers in Physics2296-424X2019-11-01710.3389/fphy.2019.00197499605Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-FractionalWei Gao0Hajar F. Ismael1Hajar F. Ismael2Sizar A. Mohammed3Haci Mehmet Baskonus4Hasan Bulut5School of Information Science and Technology, Yunnan Normal University, Kunming, ChinaDepartment of Mathematics, Faculty of Science, University of Zakho, Zakho, IraqDepartment of Mathematics, Faculty of Science, Firat University, Elâzig, TurkeyDepartment of Mathematics, College of Basic Education, University of Duhok, Duhok, IraqDepartment of Mathematics and Science Education, Harran University, Sanliurfa, TurkeyDepartment of Mathematics, Faculty of Science, Firat University, Elâzig, TurkeyIn this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.https://www.frontiersin.org/article/10.3389/fphy.2019.00197/fullparaxial wave equationcomplex solitonextended sinh-Gordon methodsoliton structurescontour surfaces
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wei Gao Hajar F. Ismael Hajar F. Ismael Sizar A. Mohammed Haci Mehmet Baskonus Hasan Bulut
spellingShingle	Wei Gao Hajar F. Ismael Hajar F. Ismael Sizar A. Mohammed Haci Mehmet Baskonus Hasan Bulut Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional Frontiers in Physics paraxial wave equation complex soliton extended sinh-Gordon method soliton structures contour surfaces
author_facet	Wei Gao Hajar F. Ismael Hajar F. Ismael Sizar A. Mohammed Haci Mehmet Baskonus Hasan Bulut
author_sort	Wei Gao
title	Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional
title_short	Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional
title_full	Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional
title_fullStr	Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional
title_full_unstemmed	Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional
title_sort	complex and real optical soliton properties of the paraxial non-linear schrödinger equation in kerr media with m-fractional
publisher	Frontiers Media S.A.
series	Frontiers in Physics
issn	2296-424X
publishDate	2019-11-01
description	In this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.
topic	paraxial wave equation complex soliton extended sinh-Gordon method soliton structures contour surfaces
url	https://www.frontiersin.org/article/10.3389/fphy.2019.00197/full
work_keys_str_mv	AT weigao complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional AT hajarfismael complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional AT hajarfismael complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional AT sizaramohammed complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional AT hacimehmetbaskonus complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional AT hasanbulut complexandrealopticalsolitonpropertiesoftheparaxialnonlinearschrodingerequationinkerrmediawithmfractional
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Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional

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