https://scholars.lib.ntu.edu.tw/handle/123456789/606445
標題: | Singular solutions of the BBM equation: analytical and numerical study | 作者: | Gavrilyuk S Shyue K.-M. KEH-MING SHYUE |
公開日期: | 2022 | 卷: | 35 | 期: | 1 | 起(迄)頁: | 388-410 | 來源出版物: | Nonlinearity | 摘要: | We show that the Benjamin–Bona–Mahony (BBM) equation admits stable travelling wave solutions representing a sharp transition from a constant state to a periodic wave train. The constant state is determined by the parameters of the periodic wave train: the wave length, amplitude and phase velocity, and satisfies both the generalized Rankine–Hugoniot conditions for the exact BBM equation and for its wave averaged counterpart. Such stable shock-like travelling structures exist if the phase velocity of the periodic wave train is not less than the solution wave averaged. To validate the accuracy of the numerical method, we derive the (singular) solitary limit of the Whitham system for the BBM equation and compare the corresponding numerical and analytical solutions. We find good agreement between analytical results and numerical solutions. ? 2021 IOP Publishing Ltd & London Mathematical Society |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85122727006&doi=10.1088%2f1361-6544%2fac3921&partnerID=40&md5=e1fa7804da5467175c4021d9a577d22c https://scholars.lib.ntu.edu.tw/handle/123456789/606445 |
ISSN: | 09517715 | DOI: | 10.1088/1361-6544/ac3921 |
顯示於: | 應用數學科學研究所 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。