{"title":"Exploration of Lie Symmetry, Bifurcation, Chaos and Exact Solution of the Geophysical KdV Equation","authors":"Badr Saad T. Alkahtani","doi":"10.1007/s10773-025-05934-6","DOIUrl":null,"url":null,"abstract":"<div><p>This research delves into a deeper investigation of the geophysical KdV equation, which is a crucial mathematical model in the study of nonlinear wave dynamics, particularly in the propagation of oceanic waves. Lie symmetry analysis is used to investigate symmetry reductions, while bifurcation and phase portrait are used to analyze the dynamic behavior. Additionally, chaos theory has been employed to examine the features of the dynamical system. Moreover, by encompassing the recent computational method, namely, the modified Sardar Sub equation (MSSE) approach, we rigorously assess the novel soliton solutions, including dark, bright, singular, combo, periodic, bright-dark, rational forms, and mixed trigonometric. It is observed that while some of the derived solutions align with existing literature, the majority of the solutions obtained in this study differ significantly from previous results, highlighting the novelty of the work. To identify chaotic characteristics, various analytical tools are utilized, such as 3D and 2D phase plots, time series analysis, multistability analysis, Poincaré maps. These findings offer significant insights into the nonlinear behavior and complex dynamics of geophysical wave models, contributing to a deeper understanding of wave propagation and chaotic systems in applied mathematics and physics.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-025-05934-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This research delves into a deeper investigation of the geophysical KdV equation, which is a crucial mathematical model in the study of nonlinear wave dynamics, particularly in the propagation of oceanic waves. Lie symmetry analysis is used to investigate symmetry reductions, while bifurcation and phase portrait are used to analyze the dynamic behavior. Additionally, chaos theory has been employed to examine the features of the dynamical system. Moreover, by encompassing the recent computational method, namely, the modified Sardar Sub equation (MSSE) approach, we rigorously assess the novel soliton solutions, including dark, bright, singular, combo, periodic, bright-dark, rational forms, and mixed trigonometric. It is observed that while some of the derived solutions align with existing literature, the majority of the solutions obtained in this study differ significantly from previous results, highlighting the novelty of the work. To identify chaotic characteristics, various analytical tools are utilized, such as 3D and 2D phase plots, time series analysis, multistability analysis, Poincaré maps. These findings offer significant insights into the nonlinear behavior and complex dynamics of geophysical wave models, contributing to a deeper understanding of wave propagation and chaotic systems in applied mathematics and physics.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.