具有箱型初始数据的Korteweg-de Vries方程中孤子-平均流的调制理论

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Ruizhi Gong, Deng-Shan Wang
{"title":"具有箱型初始数据的Korteweg-de Vries方程中孤子-平均流的调制理论","authors":"Ruizhi Gong,&nbsp;Deng-Shan Wang","doi":"10.1016/j.wavemoti.2024.103467","DOIUrl":null,"url":null,"abstract":"<div><div>For the Korteweg–de Vries equation with box type initial data, the interaction between a trial soliton and large-scale dispersive mean flow is studied theoretically and numerically. The pure box initial value can cause rarefaction wave and dispersive shock wave, and can create an area of soliton train. The key to the interaction of soliton and mean flow is that the dynamic evolutions of the mean flow and the local soliton can be described by the same modulation system. The soliton modulation system is derived from the degenerations of the two-genus Whitham modulation system. Considering the influence of rarefaction wave, dispersive shock wave and soliton train on the trial soliton, in the framework of Whitham modulation theory, the equation describing the soliton trajectory and the changes in amplitude and phase shift are given explicitly. The predicted results are compared with the numerical simulations, which verifies the corrections of the theoretical analysis. The exotic interaction phenomena between soliton and mean flow found in this work have broad applications to shallow water soliton propagations and real soliton experiments in fluid dynamics.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103467"},"PeriodicalIF":2.1000,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modulation theory of soliton−mean flow in Korteweg–de Vries equation with box type initial data\",\"authors\":\"Ruizhi Gong,&nbsp;Deng-Shan Wang\",\"doi\":\"10.1016/j.wavemoti.2024.103467\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For the Korteweg–de Vries equation with box type initial data, the interaction between a trial soliton and large-scale dispersive mean flow is studied theoretically and numerically. The pure box initial value can cause rarefaction wave and dispersive shock wave, and can create an area of soliton train. The key to the interaction of soliton and mean flow is that the dynamic evolutions of the mean flow and the local soliton can be described by the same modulation system. The soliton modulation system is derived from the degenerations of the two-genus Whitham modulation system. Considering the influence of rarefaction wave, dispersive shock wave and soliton train on the trial soliton, in the framework of Whitham modulation theory, the equation describing the soliton trajectory and the changes in amplitude and phase shift are given explicitly. The predicted results are compared with the numerical simulations, which verifies the corrections of the theoretical analysis. The exotic interaction phenomena between soliton and mean flow found in this work have broad applications to shallow water soliton propagations and real soliton experiments in fluid dynamics.</div></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"134 \",\"pages\":\"Article 103467\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524001975\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524001975","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0

摘要

对于具有箱型初始数据的Korteweg-de Vries方程,从理论上和数值上研究了试验孤子与大尺度色散平均流的相互作用。纯箱形初值可产生稀薄波和色散激波,并可形成孤子列区域。孤子与平均流相互作用的关键在于平均流与局部孤子的动态演化可以用同一个调制系统来描述。孤子调制系统是由二属惠瑟姆调制系统的退化导出的。考虑到稀疏波、色散激波和孤子列对试验孤子的影响,在Whitham调制理论的框架下,明确给出了描述试验孤子运动轨迹及幅值和相移变化的方程。将预测结果与数值模拟结果进行了比较,验证了理论分析的正确性。本文所发现的孤子与平均流之间的奇异相互作用现象在浅水孤子传播和流体动力学中的实际孤子实验中具有广泛的应用价值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modulation theory of soliton−mean flow in Korteweg–de Vries equation with box type initial data
For the Korteweg–de Vries equation with box type initial data, the interaction between a trial soliton and large-scale dispersive mean flow is studied theoretically and numerically. The pure box initial value can cause rarefaction wave and dispersive shock wave, and can create an area of soliton train. The key to the interaction of soliton and mean flow is that the dynamic evolutions of the mean flow and the local soliton can be described by the same modulation system. The soliton modulation system is derived from the degenerations of the two-genus Whitham modulation system. Considering the influence of rarefaction wave, dispersive shock wave and soliton train on the trial soliton, in the framework of Whitham modulation theory, the equation describing the soliton trajectory and the changes in amplitude and phase shift are given explicitly. The predicted results are compared with the numerical simulations, which verifies the corrections of the theoretical analysis. The exotic interaction phenomena between soliton and mean flow found in this work have broad applications to shallow water soliton propagations and real soliton experiments in fluid dynamics.
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
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
×
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