Abstract
It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves, which have been not reported for other mainstream models of shallow water waves. In this letter, the closed-form solutions of peaked solitary waves of the KdV equation, the BBM equation and the Boussinesq equation are given for the first time. All of them have either a peakon or an anti-peakon. Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and should be understood as weak solution. Therefore, the peaked solitary waves might be common for most of shallow water wave models, no matter whether or not they are integrable and/or admit breaking-wave solutions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.