Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon ex...

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Main Authors: Hemen Dutta, Hatıra Günerhan, Karmina K. Ali, Resat Yilmazer
Format: Article
Language:English
Published: Frontiers Media S.A. 2020-03-01
Series:Frontiers in Physics
Subjects:
Online Access:https://www.frontiersin.org/article/10.3389/fphy.2020.00062/full
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spelling doaj-8c774be8e1fc498a94c7bcad51afb1282020-11-25T00:45:23ZengFrontiers Media S.A.Frontiers in Physics2296-424X2020-03-01810.3389/fphy.2020.00062516070Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable DerivativeHemen Dutta0Hatıra Günerhan1Karmina K. Ali2Karmina K. Ali3Resat Yilmazer4Department of Mathematics, Gauhati University, Guwahati, IndiaDepartment of Mathematics, Faculty of Education, Kafkas University, Kars, TurkeyDepartment of Mathematics, Faculty of Science, University of Zakho, Zakho, IraqDepartment of Mathematics, Faculty of Science, Firat University, Elazig, TurkeyDepartment of Mathematics, Faculty of Science, Firat University, Elazig, TurkeyThe research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the non-linear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.https://www.frontiersin.org/article/10.3389/fphy.2020.00062/fullthe non-linear cubic-quartic Schrödinger equationconformable derivativeanalytical solutionsthe extended sinh-Gordon expansion methodsolitary wave solutions
collection DOAJ
language English
format Article
sources DOAJ
author Hemen Dutta
Hatıra Günerhan
Karmina K. Ali
Karmina K. Ali
Resat Yilmazer
spellingShingle Hemen Dutta
Hatıra Günerhan
Karmina K. Ali
Karmina K. Ali
Resat Yilmazer
Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
Frontiers in Physics
the non-linear cubic-quartic Schrödinger equation
conformable derivative
analytical solutions
the extended sinh-Gordon expansion method
solitary wave solutions
author_facet Hemen Dutta
Hatıra Günerhan
Karmina K. Ali
Karmina K. Ali
Resat Yilmazer
author_sort Hemen Dutta
title Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
title_short Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
title_full Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
title_fullStr Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
title_full_unstemmed Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative
title_sort exact soliton solutions to the cubic-quartic non-linear schrödinger equation with conformable derivative
publisher Frontiers Media S.A.
series Frontiers in Physics
issn 2296-424X
publishDate 2020-03-01
description The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the non-linear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.
topic the non-linear cubic-quartic Schrödinger equation
conformable derivative
analytical solutions
the extended sinh-Gordon expansion method
solitary wave solutions
url https://www.frontiersin.org/article/10.3389/fphy.2020.00062/full
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AT hatıragunerhan exactsolitonsolutionstothecubicquarticnonlinearschrodingerequationwithconformablederivative
AT karminakali exactsolitonsolutionstothecubicquarticnonlinearschrodingerequationwithconformablederivative
AT karminakali exactsolitonsolutionstothecubicquarticnonlinearschrodingerequationwithconformablederivative
AT resatyilmazer exactsolitonsolutionstothecubicquarticnonlinearschrodingerequationwithconformablederivative
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