分形扎哈罗夫-库兹涅佐夫-本杰明-博纳-马霍尼方程:广义变分原理和半域解

Fractals Pub Date : 2024-05-23 DOI:10.1142/s0218348x24500798
KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XU
{"title":"分形扎哈罗夫-库兹涅佐夫-本杰明-博纳-马霍尼方程:广义变分原理和半域解","authors":"KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XU","doi":"10.1142/s0218348x24500798","DOIUrl":null,"url":null,"abstract":"<p>By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions are also explored by applying the variational approach and the one-step method namely Wang’s direct mapping method-II. The dynamics of the extracted solutions on the Cantor set are unveiled graphically. The findings of this study are expected to provide some new insights into the exploration of the fractal PDEs.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"THE FRACTAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION: GENERALIZED VARIATIONAL PRINCIPLE AND THE SEMI-DOMAIN SOLUTIONS\",\"authors\":\"KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XU\",\"doi\":\"10.1142/s0218348x24500798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions are also explored by applying the variational approach and the one-step method namely Wang’s direct mapping method-II. The dynamics of the extracted solutions on the Cantor set are unveiled graphically. The findings of this study are expected to provide some new insights into the exploration of the fractal PDEs.</p>\",\"PeriodicalId\":501262,\"journal\":{\"name\":\"Fractals\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractals\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x24500798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x24500798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

通过 He 的分形导数,本文提取了一个新的分形 (2 + 1) 维扎哈罗夫-库兹涅佐夫-本杰明-博纳-马霍尼方程。本文采用半逆方法建立了广义分形变分原理。广义分形变分原理可以在分形空间中通过能量形式显示守恒定律。此外,还应用变分法和一步法(即王氏直接映射法-II)探索了一些半域解。提取的解在康托尔集上的动态变化以图形的形式展现出来。本研究的发现有望为分形多项式的探索提供一些新的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
THE FRACTAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION: GENERALIZED VARIATIONAL PRINCIPLE AND THE SEMI-DOMAIN SOLUTIONS

By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions are also explored by applying the variational approach and the one-step method namely Wang’s direct mapping method-II. The dynamics of the extracted solutions on the Cantor set are unveiled graphically. The findings of this study are expected to provide some new insights into the exploration of the fractal PDEs.

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
自引率
0.00%
发文量
0
×
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