{"title":"Investigation of New Solitary Wave Solutions of the Gilson-Pickering Equation Using Advanced Computational Techniques","authors":"M. M. Abelazeem, Raghda A. M. Attia","doi":"10.1142/s0218348x2340203x","DOIUrl":null,"url":null,"abstract":"This study focuses on employing recent and accurate computational techniques, specifically the Sardar-sub equation [Formula: see text] method, to explore novel solitary wave solutions of the Gilson–Pickering [Formula: see text] equation. The GP equation is a mathematical model with implications in fluid dynamics and wave phenomena. It describes the behavior of solitary waves, which are localized disturbances propagating through a medium without changing shape. The physical significance of the [Formula: see text] equation lies in its ability to capture the dynamics of solitary waves in various systems, including water waves, optical fibers, and nonlinear acoustic waves. The study’s findings contribute to the advancement of mathematical modeling approaches and offer valuable insights into solitary wave phenomena. The stability of the constructed solutions is investigated using the properties of the Hamiltonian system. The accuracy of the computational solutions is demonstrated by comparing them with approximate solutions obtained through He’s variational iteration [Formula: see text] method. Furthermore, the effectiveness of the employed computational techniques is validated through comparisons with other existing methods.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 3-4","pages":"0"},"PeriodicalIF":3.3000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x2340203x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This study focuses on employing recent and accurate computational techniques, specifically the Sardar-sub equation [Formula: see text] method, to explore novel solitary wave solutions of the Gilson–Pickering [Formula: see text] equation. The GP equation is a mathematical model with implications in fluid dynamics and wave phenomena. It describes the behavior of solitary waves, which are localized disturbances propagating through a medium without changing shape. The physical significance of the [Formula: see text] equation lies in its ability to capture the dynamics of solitary waves in various systems, including water waves, optical fibers, and nonlinear acoustic waves. The study’s findings contribute to the advancement of mathematical modeling approaches and offer valuable insights into solitary wave phenomena. The stability of the constructed solutions is investigated using the properties of the Hamiltonian system. The accuracy of the computational solutions is demonstrated by comparing them with approximate solutions obtained through He’s variational iteration [Formula: see text] method. Furthermore, the effectiveness of the employed computational techniques is validated through comparisons with other existing methods.
期刊介绍:
The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes.
Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.
The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.