{"title":"The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model","authors":"Chunyan Liu","doi":"10.1515/phys-2024-0069","DOIUrl":null,"url":null,"abstract":"In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the conformable extended Korteweg–de-Vries (KdV) model are investigated. First, the conformal fractional order extended KdV model is transformed into ordinary differential equation through traveling wave transformation. Second, two-dimensional (2D) planar dynamical system is presented and its chaotic behavior is studied by using the planar dynamical system method. Moreover, some three-dimensional (3D), 2D phase portraits and the Lyapunov exponent diagram are drawn. Finally, many meaningful solutions are constructed by using the complete discriminant system method, which include rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. In order to facilitate readers to see the impact of fractional order changes more intuitively, Maple software is used to draw 2D graphics, 3D graphics, density plots, contour plots, and comparison charts of some obtained solutions.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1515/phys-2024-0069","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the conformable extended Korteweg–de-Vries (KdV) model are investigated. First, the conformal fractional order extended KdV model is transformed into ordinary differential equation through traveling wave transformation. Second, two-dimensional (2D) planar dynamical system is presented and its chaotic behavior is studied by using the planar dynamical system method. Moreover, some three-dimensional (3D), 2D phase portraits and the Lyapunov exponent diagram are drawn. Finally, many meaningful solutions are constructed by using the complete discriminant system method, which include rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. In order to facilitate readers to see the impact of fractional order changes more intuitively, Maple software is used to draw 2D graphics, 3D graphics, density plots, contour plots, and comparison charts of some obtained solutions.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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