{"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, 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, 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}
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.
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.