Abstract
In this paper we consider the decay rate of solitary-wave solutions to some classes of non-linear and non-local dispersive equations, including for example the Whitham equation and a Whitham–Boussinesq system. The dispersive term is represented by a Fourier multiplier operator that has a real analytic symbol that either decays/grows, and we show that all supercritical/subcritical solitary-wave solutions decay exponentially, and moreover provide the exact decay rate, which in general will depend on the speed of the wave. We also prove that solitary waves have only one crest and are symmetric for some class of equations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
