确定(2+1)维弱耦合B型Kadomtsev-Petrviashvili方程闭式解、最优系统和各种波形的不变性分析

IF 13 1区 工程技术 Q1 ENGINEERING, MARINE
Setu Rani , Sachin Kumar , Raj Kumar
{"title":"确定(2+1)维弱耦合B型Kadomtsev-Petrviashvili方程闭式解、最优系统和各种波形的不变性分析","authors":"Setu Rani ,&nbsp;Sachin Kumar ,&nbsp;Raj Kumar","doi":"10.1016/j.joes.2021.12.007","DOIUrl":null,"url":null,"abstract":"<div><p>In the case of negligible viscosity and surface tension, the B-KP equation shows the evolution of quasi-one-dimensional shallow-water waves, and it is growingly used in ocean physics, marine engineering, plasma physics, optical fibers, surface and internal oceanic waves, Bose-Einstein condensation, ferromagnetics, and string theory. Due to their importance and applications, many features and characteristics have been investigated. In this work, we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method. First, an optimal system based on one-dimensional subalgebras is constructed, and then all possible geometric vector yields are achieved. We can reduce system order by employing the one-dimensional optimal system. Furthermore, similarity reductions and exact solutions of the reduced equations, which include arbitrary independent functional parameters, have been derived. These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics. Several three-dimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries. Various new solitary waves, kink waves, multiple solitons, stripe soliton, and singular waveforms, as well as their propagation, have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation. Lie classical method is thus a powerful, robust, and fundamental scientific tool for dealing with NPDEs. Computational simulations are also used to prove the effectiveness of the proposed approach.</p></div>","PeriodicalId":48514,"journal":{"name":"Journal of Ocean Engineering and Science","volume":null,"pages":null},"PeriodicalIF":13.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations\",\"authors\":\"Setu Rani ,&nbsp;Sachin Kumar ,&nbsp;Raj Kumar\",\"doi\":\"10.1016/j.joes.2021.12.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the case of negligible viscosity and surface tension, the B-KP equation shows the evolution of quasi-one-dimensional shallow-water waves, and it is growingly used in ocean physics, marine engineering, plasma physics, optical fibers, surface and internal oceanic waves, Bose-Einstein condensation, ferromagnetics, and string theory. Due to their importance and applications, many features and characteristics have been investigated. In this work, we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method. First, an optimal system based on one-dimensional subalgebras is constructed, and then all possible geometric vector yields are achieved. We can reduce system order by employing the one-dimensional optimal system. Furthermore, similarity reductions and exact solutions of the reduced equations, which include arbitrary independent functional parameters, have been derived. These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics. Several three-dimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries. Various new solitary waves, kink waves, multiple solitons, stripe soliton, and singular waveforms, as well as their propagation, have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation. Lie classical method is thus a powerful, robust, and fundamental scientific tool for dealing with NPDEs. Computational simulations are also used to prove the effectiveness of the proposed approach.</p></div>\",\"PeriodicalId\":48514,\"journal\":{\"name\":\"Journal of Ocean Engineering and Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":13.0000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Ocean Engineering and Science\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2468013321001406\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MARINE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Ocean Engineering and Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468013321001406","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MARINE","Score":null,"Total":0}
引用次数: 9

摘要

在粘性和表面张力可忽略的情况下,B-KP方程显示了准一维浅水波的演化,它在海洋物理学、海洋工程、等离子体物理学、光纤、表面和内部海浪、玻色-爱因斯坦凝聚、铁磁性和弦论中得到了越来越多的应用。由于它们的重要性和应用,人们已经研究了许多特征和特性。在这项工作中,我们试图使用李经典方法对弱耦合的B型Kadomtsev Petviashvili方程进行李对称性约简和闭式解。首先,构造了一个基于一维子代数的最优系统,然后获得了所有可能的几何向量产率。我们可以通过使用一维最优系统来降低系统阶数。此外,还导出了包含任意独立函数参数的简化方程的相似性约简和精确解。这些新建立的解可以增强我们对不同非线性波动现象和动力学的理解。使用几种三维和二维图形表示来确定所产生的具有确定参数的解的视觉影响,以展示它们在各种李对称性示例中的动态波形。对于弱耦合的B型Kadomtsev Petviashvili方程,已经证明了各种新的孤立波、扭结波、多孤子、条纹孤子和奇异波形及其传播。因此,李经典方法是处理NPDE的一种强大、稳健和基本的科学工具。计算仿真也被用来证明所提出的方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations

In the case of negligible viscosity and surface tension, the B-KP equation shows the evolution of quasi-one-dimensional shallow-water waves, and it is growingly used in ocean physics, marine engineering, plasma physics, optical fibers, surface and internal oceanic waves, Bose-Einstein condensation, ferromagnetics, and string theory. Due to their importance and applications, many features and characteristics have been investigated. In this work, we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method. First, an optimal system based on one-dimensional subalgebras is constructed, and then all possible geometric vector yields are achieved. We can reduce system order by employing the one-dimensional optimal system. Furthermore, similarity reductions and exact solutions of the reduced equations, which include arbitrary independent functional parameters, have been derived. These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics. Several three-dimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries. Various new solitary waves, kink waves, multiple solitons, stripe soliton, and singular waveforms, as well as their propagation, have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation. Lie classical method is thus a powerful, robust, and fundamental scientific tool for dealing with NPDEs. Computational simulations are also used to prove the effectiveness of the proposed approach.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
11.50
自引率
19.70%
发文量
224
审稿时长
29 days
期刊介绍: The Journal of Ocean Engineering and Science (JOES) serves as a platform for disseminating original research and advancements in the realm of ocean engineering and science. JOES encourages the submission of papers covering various aspects of ocean engineering and science.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信