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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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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