{"title":"无界域上分数空间耦合惠瑟姆-布罗尔-考普方程的傅立叶谱法","authors":"Li-Fang Zhao, Wei Zhang","doi":"10.1515/phys-2024-0071","DOIUrl":null,"url":null,"abstract":"Due to the nonlocality of fractional derivatives, the numerical methods for solving nonlinear fractional Whitham–Broer–Kaup (WBK) equations are time-consuming and tedious. Therefore, it is a research hotspot to explore the numerical solution of fractional-order WBK equation. The main goal of this study is to provide an efficient method for the fractional-in-space coupled WBK equations on unbounded domain and discover some novel anomalous transmission behaviors. First, the numerical solution is compared with the exact solution to determine the validity of the proposed method on large time-spatial domain. Then, anomalous transmission of waves propagation of the fractional WBK equation is numerically simulated, and the influence of different fractional-order derivatives on wave propagation of the WBK equation is researched. Some novel anomalous transmission behaviors of wave propagation of the fractional WBK equation on unbounded domain are shown.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain\",\"authors\":\"Li-Fang Zhao, Wei Zhang\",\"doi\":\"10.1515/phys-2024-0071\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Due to the nonlocality of fractional derivatives, the numerical methods for solving nonlinear fractional Whitham–Broer–Kaup (WBK) equations are time-consuming and tedious. Therefore, it is a research hotspot to explore the numerical solution of fractional-order WBK equation. The main goal of this study is to provide an efficient method for the fractional-in-space coupled WBK equations on unbounded domain and discover some novel anomalous transmission behaviors. First, the numerical solution is compared with the exact solution to determine the validity of the proposed method on large time-spatial domain. Then, anomalous transmission of waves propagation of the fractional WBK equation is numerically simulated, and the influence of different fractional-order derivatives on wave propagation of the WBK equation is researched. Some novel anomalous transmission behaviors of wave propagation of the fractional WBK equation on unbounded domain are shown.\",\"PeriodicalId\":48710,\"journal\":{\"name\":\"Open Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1515/phys-2024-0071\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1515/phys-2024-0071","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
Due to the nonlocality of fractional derivatives, the numerical methods for solving nonlinear fractional Whitham–Broer–Kaup (WBK) equations are time-consuming and tedious. Therefore, it is a research hotspot to explore the numerical solution of fractional-order WBK equation. The main goal of this study is to provide an efficient method for the fractional-in-space coupled WBK equations on unbounded domain and discover some novel anomalous transmission behaviors. First, the numerical solution is compared with the exact solution to determine the validity of the proposed method on large time-spatial domain. Then, anomalous transmission of waves propagation of the fractional WBK equation is numerically simulated, and the influence of different fractional-order derivatives on wave propagation of the WBK equation is researched. Some novel anomalous transmission behaviors of wave propagation of the fractional WBK equation on unbounded domain are shown.
期刊介绍:
Open Physics is a peer-reviewed, open access, electronic journal devoted to the publication of fundamental research results in all fields of physics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.