具有平滑/非平滑初始数据的旋转二分量卡马萨-霍尔姆系统的完全保守差分方案

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2024-04-30 DOI:10.1016/j.wavemoti.2024.103333

Tong Yan , Jiwei Zhang , Qifeng Zhang

{"title":"具有平滑/非平滑初始数据的旋转二分量卡马萨-霍尔姆系统的完全保守差分方案","authors":"Tong Yan , Jiwei Zhang , Qifeng Zhang","doi":"10.1016/j.wavemoti.2024.103333","DOIUrl":null,"url":null,"abstract":"<div><p>This paper derives a semi-discrete conservative difference scheme for the rotation-two-component Camassa–Holm system based on its Hamiltonian invariants. Mass, momentum and energy are preserved for the semi-discrete scheme. Furthermore, a fully discrete finite difference scheme is proposed without destroying any one of the conservative laws. Combining a nonlinear iteration with a threshold strategy, the accuracy of the scheme is guaranteed. Meanwhile, this scheme captures the formation and propagation of solitary wave solutions in long time behavior under smooth/nonsmooth initial data. Remarkably, a new type of asymmetric wave breaking phenomenon is revealed in the case of the nonzero rotational parameter.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"129 ","pages":"Article 103333"},"PeriodicalIF":2.1000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fully conservative difference schemes for the rotation-two-component Camassa–Holm system with smooth/nonsmooth initial data\",\"authors\":\"Tong Yan , Jiwei Zhang , Qifeng Zhang\",\"doi\":\"10.1016/j.wavemoti.2024.103333\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper derives a semi-discrete conservative difference scheme for the rotation-two-component Camassa–Holm system based on its Hamiltonian invariants. Mass, momentum and energy are preserved for the semi-discrete scheme. Furthermore, a fully discrete finite difference scheme is proposed without destroying any one of the conservative laws. Combining a nonlinear iteration with a threshold strategy, the accuracy of the scheme is guaranteed. Meanwhile, this scheme captures the formation and propagation of solitary wave solutions in long time behavior under smooth/nonsmooth initial data. Remarkably, a new type of asymmetric wave breaking phenomenon is revealed in the case of the nonzero rotational parameter.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"129 \",\"pages\":\"Article 103333\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-04-30\",\"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/S0165212524000635\",\"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/S0165212524000635","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

本文根据旋转两分量卡玛萨-霍姆系统的哈密顿不变式，推导出了该系统的半离散保守差分方案。半离散方案保留了质量、动量和能量。此外，还提出了一种完全离散的有限差分方案，而不会破坏任何一个保守定律。结合非线性迭代和阈值策略，该方案的精度得到了保证。同时，该方案捕捉到了光滑/非光滑初始数据下孤波解在长时间行为中的形成和传播。值得注意的是，在旋转参数不为零的情况下，揭示了一种新型的非对称破波现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fully conservative difference schemes for the rotation-two-component Camassa–Holm system with smooth/nonsmooth initial data

This paper derives a semi-discrete conservative difference scheme for the rotation-two-component Camassa–Holm system based on its Hamiltonian invariants. Mass, momentum and energy are preserved for the semi-discrete scheme. Furthermore, a fully discrete finite difference scheme is proposed without destroying any one of the conservative laws. Combining a nonlinear iteration with a threshold strategy, the accuracy of the scheme is guaranteed. Meanwhile, this scheme captures the formation and propagation of solitary wave solutions in long time behavior under smooth/nonsmooth initial data. Remarkably, a new type of asymmetric wave breaking phenomenon is revealed in the case of the nonzero rotational parameter.

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 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.