Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method

Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method

In this paper, we examine a modified auxiliary equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential equ...

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Main Authors: Mostafa M. A. Khater, Dianchen Lu, Raghda A. M. Attia
Format: Article
Language:English
Published: AIP Publishing LLC 2019-02-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.5087647
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spelling doaj-7d520b35f89f4234940c59681d802ee62020-11-24T22:01:57ZengAIP Publishing LLCAIP Advances2158-32262019-02-0192025003025003-810.1063/1.5087647005902ADVDispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation methodMostafa M. A. Khater0Dianchen Lu1Raghda A. M. Attia2Department of Mathematics, Faculty of Science, Jiangsu University, 212013, ChinaDepartment of Mathematics, Faculty of Science, Jiangsu University, 212013, ChinaDepartment of Mathematics, Faculty of Science, Jiangsu University, 212013, ChinaIn this paper, we examine a modified auxiliary equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential equations. We used conformable derivatives properties to convert nonlinear fractional partial differential equation into the ordinary differential equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.http://dx.doi.org/10.1063/1.5087647
collection DOAJ
language English
format Article
sources DOAJ
author Mostafa M. A. Khater
Dianchen Lu
Raghda A. M. Attia
spellingShingle Mostafa M. A. Khater
Dianchen Lu
Raghda A. M. Attia
Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
AIP Advances
author_facet Mostafa M. A. Khater
Dianchen Lu
Raghda A. M. Attia
author_sort Mostafa M. A. Khater
title Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
title_short Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
title_full Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
title_fullStr Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
title_full_unstemmed Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
title_sort dispersive long wave of nonlinear fractional wu-zhang system via a modified auxiliary equation method
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2019-02-01
description In this paper, we examine a modified auxiliary equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential equations. We used conformable derivatives properties to convert nonlinear fractional partial differential equation into the ordinary differential equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.
url http://dx.doi.org/10.1063/1.5087647
work_keys_str_mv AT mostafamakhater dispersivelongwaveofnonlinearfractionalwuzhangsystemviaamodifiedauxiliaryequationmethod
AT dianchenlu dispersivelongwaveofnonlinearfractionalwuzhangsystemviaamodifiedauxiliaryequationmethod
AT raghdaamattia dispersivelongwaveofnonlinearfractionalwuzhangsystemviaamodifiedauxiliaryequationmethod
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