Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations

In this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existe...

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Main Authors:	Younis Muhammad, Ali Safdar
Format:	Article
Language:	English
Published:	De Gruyter 2015-02-01
Series:	Open Engineering
Subjects:	Solitary wave solution shock wave solution (1+1)-dimensional perturbed Klein-Gordon equation (1+1)-dimensional Kaup-Keperschmidt equation (2+1)- dimentional ZK-BBM equation solitary wave ansatz
Online Access:	http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0014/eng-2015-0014.xml?format=INT

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spelling	doaj-95f95df2499449bab97c7ba2ae16cc952020-11-24T20:48:15ZengDe GruyterOpen Engineering2391-54392015-02-015110.1515/eng-2015-0014eng-2015-0014Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equationsYounis Muhammad0Ali Safdar1Muhammad Younis: Centre for Undergraduate Studies, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, Minhaj University, Lahore, PakistanIn this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existence of the solitons are identified during the derivation of the solution. Since, the nonlinear wave is one of the fundamental object of nature and a growing interest has been given to the propagation of nonlinear wave in dynamical system.http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0014/eng-2015-0014.xml?format=INTSolitary wave solution shock wave solution (1+1)-dimensional perturbed Klein-Gordon equation (1+1)-dimensional Kaup-Keperschmidt equation (2+1)- dimentional ZK-BBM equation solitary wave ansatz
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Younis Muhammad Ali Safdar
spellingShingle	Younis Muhammad Ali Safdar Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations Open Engineering Solitary wave solution shock wave solution (1+1)-dimensional perturbed Klein-Gordon equation (1+1)-dimensional Kaup-Keperschmidt equation (2+1)- dimentional ZK-BBM equation solitary wave ansatz
author_facet	Younis Muhammad Ali Safdar
author_sort	Younis Muhammad
title	Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations
title_short	Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations
title_full	Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations
title_fullStr	Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations
title_full_unstemmed	Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations
title_sort	solitary wave and shock wave solutions of (1+1)-dimensional perturbed klein-gordon,(1+1)-dimensional kaup-keperschmidt and (2+1)-dimensional zk-bbm equations
publisher	De Gruyter
series	Open Engineering
issn	2391-5439
publishDate	2015-02-01
description	In this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existence of the solitons are identified during the derivation of the solution. Since, the nonlinear wave is one of the fundamental object of nature and a growing interest has been given to the propagation of nonlinear wave in dynamical system.
topic	Solitary wave solution shock wave solution (1+1)-dimensional perturbed Klein-Gordon equation (1+1)-dimensional Kaup-Keperschmidt equation (2+1)- dimentional ZK-BBM equation solitary wave ansatz
url	http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0014/eng-2015-0014.xml?format=INT
work_keys_str_mv	AT younismuhammad solitarywaveandshockwavesolutionsof11dimensionalperturbedkleingordon11dimensionalkaupkeperschmidtand21dimensionalzkbbmequations AT alisafdar solitarywaveandshockwavesolutionsof11dimensionalperturbedkleingordon11dimensionalkaupkeperschmidtand21dimensionalzkbbmequations
_version_	1716808407518806016

Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations

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