$G$-Strands and Peakon Collisions on $\mathrm{Diff}(\mathbb{R})$

Darryl D. Holm, Rossen I. Ivanov

A $G$-strand is a map $g:\mathbb{R}\times \mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. Some $G$-stra…