Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics

Solitary wave profiles of various forms can be found in many disciplines, including oceanography, marine engineering, plasma physics, optical fibers, fluid dynamics, and mathematical sciences. In this work, we use the generalized exponential rational function (GERF) method to find the closed-form wa...

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Autores principales:	Sachin Kumar, Monika Niwas, Nikita Mann
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Closed-form solutions ZK-BBM and GZK-BBM equations GERF method Dark and bright solitons Nonlinear evolution equations Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/d3bf5f398ccb40e3ae25903241cfb4dc
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spelling	oai:doaj.org-article:d3bf5f398ccb40e3ae25903241cfb4dc2021-11-24T04:35:04ZAbundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics2666-818110.1016/j.padiff.2021.100200https://doaj.org/article/d3bf5f398ccb40e3ae25903241cfb4dc2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666818121001042https://doaj.org/toc/2666-8181Solitary wave profiles of various forms can be found in many disciplines, including oceanography, marine engineering, plasma physics, optical fibers, fluid dynamics, and mathematical sciences. In this work, we use the generalized exponential rational function (GERF) method to find the closed-form wave solutions to two nonlinear evolution equations, the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZK-BBM) equation, and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZK-BBM) equation. The GERF method under the wave transformation is a very simple, efficient, robust, and straightforward technique for solving various nonlinear partial differential equations. By utilizing this technique, we obtain thirty different kinds of exact solitary wave solutions for governing equations. These newly solitary wave solutions are generated in terms of the rational function, trigonometric function, hyperbolic function, and exponential function forms, all of which play crucial roles in many areas of nonlinear sciences and engineering. Furthermore, we present the two-dimensional and three-dimensional wave profiles of some achieved solutions under the best suitable choices of involved arbitrary constants with dependable range space to understand the dynamical wave behaviors of the solutions, which makes this research more commendable. The GZK-BBM equation demonstrates how the model behaves when long waves propagate, which has a nonlinear and dissipative impact.Sachin KumarMonika NiwasNikita MannElsevierarticleClosed-form solutionsZK-BBM and GZK-BBM equationsGERF methodDark and bright solitonsNonlinear evolution equationsApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100200- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Closed-form solutions ZK-BBM and GZK-BBM equations GERF method Dark and bright solitons Nonlinear evolution equations Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Closed-form solutions ZK-BBM and GZK-BBM equations GERF method Dark and bright solitons Nonlinear evolution equations Applied mathematics. Quantitative methods T57-57.97 Sachin Kumar Monika Niwas Nikita Mann Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
description	Solitary wave profiles of various forms can be found in many disciplines, including oceanography, marine engineering, plasma physics, optical fibers, fluid dynamics, and mathematical sciences. In this work, we use the generalized exponential rational function (GERF) method to find the closed-form wave solutions to two nonlinear evolution equations, the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZK-BBM) equation, and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZK-BBM) equation. The GERF method under the wave transformation is a very simple, efficient, robust, and straightforward technique for solving various nonlinear partial differential equations. By utilizing this technique, we obtain thirty different kinds of exact solitary wave solutions for governing equations. These newly solitary wave solutions are generated in terms of the rational function, trigonometric function, hyperbolic function, and exponential function forms, all of which play crucial roles in many areas of nonlinear sciences and engineering. Furthermore, we present the two-dimensional and three-dimensional wave profiles of some achieved solutions under the best suitable choices of involved arbitrary constants with dependable range space to understand the dynamical wave behaviors of the solutions, which makes this research more commendable. The GZK-BBM equation demonstrates how the model behaves when long waves propagate, which has a nonlinear and dissipative impact.
format	article
author	Sachin Kumar Monika Niwas Nikita Mann
author_facet	Sachin Kumar Monika Niwas Nikita Mann
author_sort	Sachin Kumar
title	Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
title_short	Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
title_full	Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
title_fullStr	Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
title_full_unstemmed	Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics
title_sort	abundant analytical closed-form solutions and various solitonic wave forms to the zk-bbm and gzk-bbm equations in fluids and plasma physics
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/d3bf5f398ccb40e3ae25903241cfb4dc
work_keys_str_mv	AT sachinkumar abundantanalyticalclosedformsolutionsandvarioussolitonicwaveformstothezkbbmandgzkbbmequationsinfluidsandplasmaphysics AT monikaniwas abundantanalyticalclosedformsolutionsandvarioussolitonicwaveformstothezkbbmandgzkbbmequationsinfluidsandplasmaphysics AT nikitamann abundantanalyticalclosedformsolutionsandvarioussolitonicwaveformstothezkbbmandgzkbbmequationsinfluidsandplasmaphysics
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Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics

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