{"title":"探索 (2+1) 维的多孑子模式、分岔分析和混沌：非线性动力学研究","authors":"Ziyad A. Alhussain","doi":"10.1016/j.asej.2024.102917","DOIUrl":null,"url":null,"abstract":"<div><p>This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models.</p></div>","PeriodicalId":48648,"journal":{"name":"Ain Shams Engineering Journal","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2090447924002922/pdfft?md5=4547af2a2183057a593ba3ec3fab9255&pid=1-s2.0-S2090447924002922-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Exploring multi-soliton patterns, bifurcation analysis, and chaos in (2+1) dimensions: A study on nonlinear dynamics\",\"authors\":\"Ziyad A. Alhussain\",\"doi\":\"10.1016/j.asej.2024.102917\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models.</p></div>\",\"PeriodicalId\":48648,\"journal\":{\"name\":\"Ain Shams Engineering Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2090447924002922/pdfft?md5=4547af2a2183057a593ba3ec3fab9255&pid=1-s2.0-S2090447924002922-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ain Shams Engineering Journal\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2090447924002922\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ain Shams Engineering Journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2090447924002922","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Exploring multi-soliton patterns, bifurcation analysis, and chaos in (2+1) dimensions: A study on nonlinear dynamics
This study explores the intrinsic characteristics of the (2+1)-dimensional Schwarz-Korteweg-de Vries equation used to describe shallow water waves. The multiple solitons are successfully constructed using a technique involving multiple exponential functions. Graphical representations of the results are provided in 3D, 2D, and density plots to assess the compatibility of the solutions. Also, the dynamic nature of studied equation is examined based on bifurcation and chaos theory for nonlinear systems. Bifurcation signifies how our dynamical system is affected by physical parameters in planar dynamical system. After that, we apply the external force on planar dynamical system to show the chaotic like behavior of the studied model. Such behavior is confirmed by utilizing different chaos detecting tools. The obtained results serve to explain the effectiveness and applicability of the utilized methodologies in comprehend the exact solution and qualitative behavior of nonlinear physical models.
期刊介绍：
in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance.
Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
