On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative

The aim of this paper is to introduce a novel study of obtaining exact solutions to the (2+1) - dimensional conformable KdV equation modeling the amplitude of the shallow-water waves in fluids or electrostatic wave potential in plasmas. The reduction of the governing equation to a simpler ordinary d...

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Autores principales:	Özkan Yeşim Sağlam, Yaşar Emrullah, Çelik Nisa
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	solitons korteweg-de vries equation exact solutions improved tan(φ/2)-expansion method jacobi elliptic function expansion method Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/7e4fe606d6b84906a4be1af2f8832327
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spelling	oai:doaj.org-article:7e4fe606d6b84906a4be1af2f88323272021-12-05T14:10:57ZOn the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative2192-80102192-802910.1515/nleng-2021-0005https://doaj.org/article/7e4fe606d6b84906a4be1af2f88323272021-04-01T00:00:00Zhttps://doi.org/10.1515/nleng-2021-0005https://doaj.org/toc/2192-8010https://doaj.org/toc/2192-8029The aim of this paper is to introduce a novel study of obtaining exact solutions to the (2+1) - dimensional conformable KdV equation modeling the amplitude of the shallow-water waves in fluids or electrostatic wave potential in plasmas. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. By using the improved tan(φ/2)-expansion method (ITEM) and Jacobi elliptic function expansion method, exact solutions including the hyperbolic function solution, rational function solution, soliton solution, traveling wave solution, and periodic wave solution of the considered equation have been obtained. We achieve also a numerical solution corresponding to the initial value problem by conformable variational iteration method (C-VIM) and give comparative results in tables. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.Özkan Yeşim SağlamYaşar EmrullahÇelik NisaDe Gruyterarticlesolitonskorteweg-de vries equationexact solutionsimproved tan(φ/2)-expansion methodjacobi elliptic function expansion methodEngineering (General). Civil engineering (General)TA1-2040ENNonlinear Engineering, Vol 10, Iss 1, Pp 46-65 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	solitons korteweg-de vries equation exact solutions improved tan(φ/2)-expansion method jacobi elliptic function expansion method Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	solitons korteweg-de vries equation exact solutions improved tan(φ/2)-expansion method jacobi elliptic function expansion method Engineering (General). Civil engineering (General) TA1-2040 Özkan Yeşim Sağlam Yaşar Emrullah Çelik Nisa On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
description	The aim of this paper is to introduce a novel study of obtaining exact solutions to the (2+1) - dimensional conformable KdV equation modeling the amplitude of the shallow-water waves in fluids or electrostatic wave potential in plasmas. The reduction of the governing equation to a simpler ordinary differential equation by wave transformation is the first step of the procedure. By using the improved tan(φ/2)-expansion method (ITEM) and Jacobi elliptic function expansion method, exact solutions including the hyperbolic function solution, rational function solution, soliton solution, traveling wave solution, and periodic wave solution of the considered equation have been obtained. We achieve also a numerical solution corresponding to the initial value problem by conformable variational iteration method (C-VIM) and give comparative results in tables. Moreover, by using Maple, some graphical simulations are done to see the behavior of these solutions with choosing the suitable parameters.
format	article
author	Özkan Yeşim Sağlam Yaşar Emrullah Çelik Nisa
author_facet	Özkan Yeşim Sağlam Yaşar Emrullah Çelik Nisa
author_sort	Özkan Yeşim Sağlam
title	On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
title_short	On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
title_full	On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
title_fullStr	On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
title_full_unstemmed	On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
title_sort	on the exact and numerical solutions to a new (2 + 1)-dimensional korteweg-de vries equation with conformable derivative
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/7e4fe606d6b84906a4be1af2f8832327
work_keys_str_mv	AT ozkanyesimsaglam ontheexactandnumericalsolutionstoanew21dimensionalkortewegdevriesequationwithconformablederivative AT yasaremrullah ontheexactandnumericalsolutionstoanew21dimensionalkortewegdevriesequationwithconformablederivative AT celiknisa ontheexactandnumericalsolutionstoanew21dimensionalkortewegdevriesequationwithconformablederivative
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On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative

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