S. K. Mohanty, A. N. Dev, S. Sahoo, H. Emadifar, G. Arora
{"title":"Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <msup>\n <mrow>\n ","authors":"S. K. Mohanty, A. N. Dev, S. Sahoo, H. Emadifar, G. Arora","doi":"10.1155/2023/3965804","DOIUrl":null,"url":null,"abstract":"In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized \n \n \n \n \n \n G\n \n \n ′\n \n \n /\n G\n \n \n \n expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized \n \n \n \n \n \n G\n \n \n ′\n \n \n /\n G\n \n \n \n expansion technique. The extended generalized \n \n \n \n \n \n G\n \n \n ′\n \n \n /\n G\n \n \n \n expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of \n \n \n \n \n \n G\n \n \n ′\n \n \n /\n G\n \n \n \n . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2023/3965804","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized
G
′
/
G
expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized
G
′
/
G
expansion technique. The extended generalized
G
′
/
G
expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of
G
′
/
G
. The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.
期刊介绍:
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike.
As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.