Abstract
We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler-Poincaré equations defined on the Virasoro-Bott group, by using the inverse map (also called 'back-to-labels' map). This family contains as special cases the well-known Korteweg-de Vries, Camassa-Holm and Hunter-Saxton soliton equations. In the conclusion section, we sketch opportunities for future work that would apply the new Clebsch momentum map with 2-cocycles derived here to investigate a new type of interplay among nonlinearity, dispersion and noise.
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 callMore From: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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.
