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تسجيل مستخدم جديدNew variational and multisymplectic formulations of the Euler-Poincare equation on the Virasoro-Bott group using the inverse map
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We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincare 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.
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